Probability

Problem 101

Bear Manufacturing makes teddy bears on an assembly line with a normal distribution of the actual weights of the bears. They have found that the mean weight of the bears is 15 ounces with a standard deviation of 0.5 ounces. These bears are sold to vendors of Wet Teddy Bear carts. These vendors have high standards for the consistency of the bears that they sell, so they have indicated that they will only accept teddy bears that weigh from 14 ounces through 16 ounces. If 20,000 teddy bears were made on the assembly line during a week, then how many teddy bears will be refused by the vendors that week? $\square$ A)

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Problem 102

In the following visual, there are eight regions labeled A through H. Use those regions to answer the following questions related to IQ. Remember, the mean is 100 and the standard deviation is 15.
In which region would an IQ of 96 fall? $\square$ A
In which region would an IQ of 135 fall? $\square$ $A \sqrt{n}$ In which regions would IQs of 70 through 115 fall? State the regions as they occur from left to right and separate with a comma and space. For example: A, B, C, D $\square$ $\sqrt[A]{ }$
In which regions would IQs above 130 fall? Select in order from left to right. $\square$ A In which regions would 95\% of all people's IQs fall? Select in order from left to right. $\square$ A What percent of all people have IQs that fall into region H? Include the percent sign with your answer. $\square$ A)

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Problem 103

The density of $X$ is given by $f(x)=\left\{\begin{array}{ll} 10 / x^{2}, & \text { for } x>10 \\ 0, & \text { for } x \leq 10 \end{array}\right.$
What is the distribution function of $X$ ? Find $P\{X>20\}$ .

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Problem 104

passengers in a car. 8.3 If you throw two dice at the same time, the probability that a six will be shown on one of the dice is $\frac{10}{36}$ and the probability that a six will be shown on both the dice, is $\frac{1}{36}$ . What is the probability that a six will NOT show on either of the dice when you throw two dice at the same time?

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Problem 105

2.2 Complete the following: 2.2.1 For exhaustive events: $\mathrm{P}(\mathrm{A}$ or B $)=\ldots$ . 2.2.2 For mutually exclusive events: $\mathrm{P}(\mathrm{A}$ and B $)=\ldots$ .

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Problem 106

Name: $\qquad$
21. [Maximum mark: 6]
Date: $\qquad$
A factory produces bags of sugar with a labelled weight of 500 g . The weights of the bags are normally distributed with a mean of 500 g and a standard deviation of 3 g . (a) [1] Write down the percentage of bags that weigh more than 500 g .
A bag that weighs less than 495 g is rejected by the factory for being underweight. (b) [2] Find the probability that a randomly chosen bag is rejected for being underweight. (c) [3] A bag that weighs more than $k$ grams is rejected by the factory for being overweight. factory rejects $2 \%$ of bags for being overweight.
Find the value of $k$ .

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Problem 107

Thee Probodility that a Sede Gered Gnt "1/3 if three of the eed planted. What, "s the proboblity to Nor-Germinaber at least Une wil gaminates Only One will Guminets

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Problem 108

A board game uses the deck of 20 cards shown to the right. Two cards are selected at random from this deck. Calculate the probability that both cards selected have a 2 , both with and without replacement.
Two cards are to be selected with replacement. Determine the probability that both cards selected have a 2. $\square$ (Type an integer or a simplified fraction.) Two cards áre to be selected without replacement. Determine the probability that both cards selected have a 2. $\square$ (Type an integer or a simplified fraction.)

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Problem 109

People with type O-negative blood are universal donors. Any patient can receive a transfusion of O-negative blood. Only 7.2\% of the American population has O-negative blood. If we choose 10 Americans at random, what is the probability that at least 1 of them has O -negative blood? $\square$ (Round to 3 decimal places. Leave your answer in decimal form.)

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Problem 110

Intersection and conditional probability
Suppose that a certain college class contains 39 students. Of these, 24 are sophomores, 21 are social science majors, and 12 are neither. A student is selected at random from the class. (a) What is the probability that the student is both a sophomore and a social science major? (b) Given that the student selected is a sophomore, what is the probability that he is also a social science major?
Write your responses as fractions. (If necessary, consult a list of formulas.) (a) $\square$ (b) $\square$ Explanation Check O 2024 MaSraw HIILC An Rights Roserved. Terms of Use 1 Privacy Center I $46^{\circ} \mathrm{F}$ Sunny Search

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Problem 111

The reading speed of second grade students in a large city is approximately normal, with a mean of 92 words per minute (wpm) and a standard deviation of 10 wpm. Complete parts (a) through (f). (a) What is the probability a randomly selected student in the city will read more than 97 words per minute?
The probability is 0.3085 (Round to four decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice A. If 100 different students were chosen from this population, we would expect to read exactly 97 words per minute B.- If 100 different students were chosen from this population, we would expect 31 to read more than 97 words per minute C. If 100 different students were chosen from this population, we would expect to read less than 97 words per minute. (b) What is the probability that a random sample of 10 second grade students from the city results in a mean reading rate of more than 97 words per minute?
The probability is $\square$ (Round to four decimal places as needed.)

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Problem 112

What is the probability a randomly selected student in the city will read more than 97 words per minute? probability is 0.3085. und to four decimal places as needed.) rpret this probability. Select the correct choice below and fill in the answer box within your choice A. If 100 different students were chosen from this population, we would expect to read exactly 97 words per minute B. If 100 different students were chosen from this population, we would expect 31 to read more than 97 words per minute C. If 100 different students were chosen from this population, we would expect to read less than 97 words per minute
What is the probability that a random sample of 10 second grade students from the city results in a mean reading rate of more than 97 words per minute? probability is 0.0571 und to four decimal places as needed.) rpret this probability. Select the correct choice below and fill in the answer box within your choice. A. If 100 independent samples of $n=10$ students were chosen from this population, we would expect $\square$ sample(s) to have a sample mean reading rate of less than 97 words per minute. B. If 100 independent samples of $n=10$ students were chosen from this population, we would expect $\square$ sample(s) to have a sample mean reading rate of exactly 97 words per minute. C. If 100 independent samples of $\mathrm{n}=10$ students were chosen from this population, we would expect $\square$ sample(s) to have a sample mean reading rate of more than 97 words per minute.

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Problem 113

You pick a coin from the bag. Then, without replacing it, pick another coin. What is the probability $Q$ of picking a quarter, then a nickel? Answer as a simplified fraction in the form a/b.

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Problem 114

3) A person's blood glucose level and diabetes are closely related. Let $x$ be a measurement in milligrams of glucose per deciliter of blood. After a 12 -hour fast, the variable x will have a distribution that is approximately normal with a mean of 85 and standard deviation of 25 . This is only true for adults under age 50 . Use this information to answer the questions that follow: a) What percentage of people have a blood glucose level less than 110? b) What percentage of people have a blood glucose level more than $120 ?$ c) What percentage of people have a blood glucose level between 100 and 125 ? 3) A survey found that people keep their television sets an average of 4.8 years. The standard deviation is 0.89 year. Find the following percentages assuming a normal distribution. a) What percent of people keep a TV less than 2.5 years? b) What percent of people keep a TV more than 4.2 years? c) What percent of people keep a TV between 3 and 4 years?

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Problem 115

Unit 2: The Normal Distribution L4 Practice - The Standard Normal Curve Name: $\qquad$ Hamahtlargus 1) Scores on the Wechsler Adult Intelligence Scale, a standard IQ test, are approximately Normal for the age group of 20 to 34 . The mean score is 110 with a standard deviation of 25 . What percent of this age group has an IQ below 100 ? $P=(-.28<z<.35)$ a) Write the inequality using the raw score. b) Find the $z$ -score and rewrite the inequality. $\text { ?. } P\left(\quad z=\frac{\frac{100-10}{25}}{z=-.4}\right.$ c) Draw the Normal standardized curve. d) What are you entering into your calculator? $z=\frac{20-110}{25}=-3.6 \quad z=\frac{34-110}{25}=-3.04$ e) $34,4 \%$ of adults from 20 to 34 have an IQ less than 100 . 2) The distribution of blood cholesterol levels in 14 -year-old boys is roughly normal; the mean is 165 milligrams of cholesterol per deciliter of blood and the standard deviation is 30 . What proportion of 14 -year-old boys have a blood cholesterol level over $120 \mathrm{mg} / \mathrm{dl}$ ? a) Write the inequality. $P 1$ c) Draw the Normal standardized curve. b) Find the $z$ -score and rewrite the inequality. $z=\frac{120-165}{30}=-1.5$ d) What are you entering into your calculator?
Lower: Upper: Mean $(\mu)$ : Standard Deviation $(\boldsymbol{\sigma})$ : e) $\qquad$ $\%$ of 14 -year-old boys have a blood cholesterol level over $120 \mathrm{mg} / \mathrm{dl}$ .

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Problem 116

You pick a card at random. 4 5 6 7
What is $\mathrm{P}($ less than 5 $)$ ? Write your answer as a percentage. $\square$ \% Submit

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Problem 117

Suppose that a life insurance company insures $1,000,000$ fifty-year-old people in a given year. (Assume a death rate of 6 per 1000 people.) The cost of the premium is $\$ 500$ per year, and the death benefit is $\$ 50,000$ . What is the expected profit or loss for the insurance company?
The insurance company can expect a(n) \\square $million$ \square$ (Type an integer or decimal rounded to one decimal place as needed.)

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Problem 118

A group of friends are playing 5 -card poker with a deck of 52 cards. For a probability distribution showing the individual probabilities of all possible hands, what would be the sum of all the individual probabilities?
Choose the correct answer below A. The sum would equal 5 because the hands have five cards. B. The sum would equal 1 because all of the friends have drawn a hand. C. The sum would equal 1 because the sum of the probabilities of all possible events in any situation is 1 D. The sum would equal 52 because there are 52 total cards. E. The sum would equal 5 because all of the friends drew five cards. F. The sum would equal 52 because 52 cards were drawn.

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Problem 119

Halfway through the season, a soccer player has made 10 penalty kicks in 17 attempts. Based on her performance to date, what is the relative frequency probability that she will make her next penalty kick?
The relative frequency probability that she will make her next penalty kick is $\square$ (Type an integer or decimal rounded to the nearest thousandth as needed.)

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Problem 120

Determine the probability of the given opposite event. What is the probability that a $50 \%$ free-throw shooter will miss her next free throw?
The probability that a $50 \%$ freethrow shooter will miss her next free throw is (Type an integer or a decimal.) $\square$

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Problem 121

Determine whether the following individual events are independent or dependent. Then find the probability of the combined event. The next ten births at a hospital all being boys.
Choose the correct answer below. (Simplify your answer.) A. The individual events are dependent. The probability of the combined event is $\square$ . B. The individual events are independent. The probability of the combined event is $\square$

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Problem 122

Determine whether the following individual events are independent or dependent. Then find the probability of the combined event. Randomly drawing and immediately eating two red pieces of candy in a row from a bag that contains 13 red pieces of candy out of 35 pieces of candy total.
Choose the correct answer below. (Round to three decimal places as needed.) A. The individual events are independent. The probability of the combined event is $\square$ B. The individual events are dependent. The probability of the combined event is $\square$

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Problem 123

Use the "at least once" rule to find the probability of the following event. Getting rain at least once in 4 days if the probability of rain on each single day is 0.2
The probability is $\square$ (Round to three decimal places as needed.)

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Problem 124

6. [0/1 Points] DETAILS MY NOTES SMITHNM13 13.2.035. PREVIOUS \\square \begin{tabular}{|c|c|c|} \hline \multirow{2}{}{$\$ 1.00$} & \multicolumn{2}{|c|}{$\$ 6.00$} \\ \cline { 2 - 2 } & \ $8.00$ & \multirow{2}{}{ $\$ 10.00$ } \\ \cline { 2 - 2 } & $\$ 4.00$ & \\ \hline \end{tabular}
Suggested tutorial: $\square$ Need Help? Rasd It

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Problem 125

According to a survey conducted at the local DMV, $45 \%$ of drivers who drive to work stated that they regularly exceed the posted speed limit on their way to work. Suppose that this result is true for the population of drivers who drive to work. A random sample of 11 drivers who drive to work is selected. Use the binomial probabilities table (Table I of Appendix B) or technology to find to 3 decimal places the probability that the number of drivers in this sample of 11 who regularly exceed the posted speed limit on their way to work is a. at most 4
Probability = b. 6 to 9
Probability $=$ $\square$ c. at least 8
Probability = $\square$

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Problem 126

5.4.3. Five hundred adults are asked whether they favor a bipartisan campaign finance reform bill. If the true proportion of the electorate in favor of the legislation is $52 \%$ , what are the chances that fewer than half of those in the sample support the proposal? Use a Z transformation to approximate the answer.

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Problem 127

19. Battery Life The length of life (in days) of an alkaline battery has an exponential distribution with an average life of 1 year, so that $\lambda=1 / 365$ . a. What is the probability that an alkaline battery will fail before 180 days?
Answer b. What is the probability that an alkaline battery will last beyond 1 year?
Answer c. If a device requires two batteries, what is the probability that both batteries last beyond 1 year?

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Problem 128

5.3.7. Five independent samples, each of size $n$ , are to be drawn from a normal distribution where $\sigma$ is known. For each sample, the interval $\left(\bar{y}-0.96 \cdot \frac{d}{\sqrt{n}}, \bar{y}+1.06 \cdot \frac{d}{\sqrt{n}}\right)$ will be constructed. What is the probability that at least four of the intervals will contain the unknown $\mu$ ?

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Problem 129

The overhead reach distances of adult females are normally distributed with a mean of 205.5 cm and a standard deviation of 8.9 cm . a. Find the probability that an individual distance is greater than 218.90 cm . b. Find the probability that the mean for 20 randomly selected distances is greater than 204.20 cm . c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30 ? a. The probability is 0.0655 . (Round to four decimal places as needed.) b. The probability is $\square$ . (Round to four decimal places as needed.)

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Problem 130

Assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of $\mu=1.2 \mathrm{~kg}$ and a standard deviation of $\sigma=4.7$ kg . Complete parts (a) through (c) below. a. If 1 male college student is randomly selected, find the probability that he gains between 0 kg and 3 kg during freshman year.
The probability is $\square$ (Round to four decimal places as needed.)

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Problem 131

Assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of $\mu=1.3 \mathrm{~kg}$ and a standard deviation of $\sigma=4.6$ kg . Complete parts (a) through (c) below. a. If 1 male college student is randomly selected, find the probability that he gains between 0 kg and 3 kg during freshman year.
The probability is $\square$ (Round to four decimal places as needed.)

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Problem 132

An elevator has a placard stating that the maximum capacity is $3500 \mathrm{lb}-25$ passengers. So, 25 adult male passengers can have a mean weight of up to $3500 / 25=140$ pounds. Assume that weights of males are normally distributed with a mean of 188 lb and a standard deviation of 33 lb . a. Find the probability that 1 randomly selected adult male has a weight greater than 140 lb. b. Find the probability that a sample of 25 randomly selected adult males has a mean weight greater than 140 lb . c. What do you conclude about the safety of this elevator? a. The probability that 1 randomly selected adult male has a weight greater than 140 lb is $\square$ (Round to four decimal places as needed.)

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Problem 133

An elevator has a placard stating that the maximum capacity is $3500 \mathrm{lb}-25$ passengers. So, 25 adult male passengors can have a mean weight of up to $3500 / 25=140$ pounds. Assume that weights of males are normally distributed with a mean of 188 lb and a standard deviation of 33 lb . a. Find the probability that 1 randomily selected adult male has a weight greater than 140 Ib. b. Find the probability that a sample of 25 randomly selected adult males has a mean weight greater than 140 lb . c. What do you conclude about the safety of this elevator? a. The probability that 1 randomly selected adult male has a weight greater than 140 lb is 0.9265. (Round to four decimal places as needed.) b. The probability that a sample of 25 randomly selected adult males has a mean weight greater than 140 lb is $\square$ . (Round to four decimal places as needed.)

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Problem 134

Let $X$ be normally distributed with mean $\mu=10$ and standard deviation $\sigma=6$ . Note: You may find it useful to reference the $z$ table. a. Find $P(X \leq 0)$ .
Note: Round your final answer to 4 decimal places. $P(X \leq 0)$ b. Find $P(X>2)$ .
Note: Round your final answer to 4 decimal places. $P(X>2)$

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Problem 135

[0/6 Points] DETAILS MY NOTES BBUNDERSTAT12HS 5.2.017.MI. PREVIOUS ANSWERS ASK YOUR TEACHER PRACTICE ANOTHER (a) Before 1918 , in a random sample of 12 wolves spotted in the region, what is the probability that 9 or more were male? 0.225
What is the probability that 9 or more were female? 0.225
What is the probability that fewer than 6 were female? 0.397 (b) For the period from 1918 to the present, in a random sample of 12 wolves spotted in the region, what is the probability that 9 or more were male? 0.099
What is the probability that 9 or more were female? 0.004
What is the probability that fewer than 6 were female? 0.789
Need Help? Road It Watch It Master It

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Problem 136

5. The following table shows music preferences found by a survey of the faculty at a local university. Express your answers in fraction form. \begin{tabular}{|l|c|c|c|c|} \hline & Country Music (C) & Rock Music (R) & Oldies (O) & Total \\ \hline Northern U.S. (N) & 11 & 88 & 49 & 148 \\ \hline Southern U.S. (S) & 70 & 50 & 44 & 164 \\ \hline Total & 81 & 138 & 93 & 312 \\ \hline \end{tabular} a. Find the probability that a randomly selected person from this group likes country music. b. What is the probability that a randomly selected person from this group likes rock music and is from the North? c. Find the probability that a randomly selected person from this group likes oldies given that they are from the South. d. Find $P(R)$ in decimal form. Round to two decimal places. e. Find $P(S)$ in decimal form. Round to two decimal places. f. Find $P(R \mid S)$ and explain if events $R$ and $S$ are independent or associated events. g. Zoe and Lisa are having a disagreement about conditional probability. Zoe thinks that $P(A \mid B)=P(B \mid A)$ for any two events $A$ and $B$ . Lisa says that $P(A \mid B)$ and $P(B \mid A)$ do not have to be equal. Pick two events from the table in problem 5 and determine who is correct.

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Problem 137

distribution below? 0.2 0.4 1 3

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Problem 138

Español
Tammy rolled a number cube 200 times and got the following results. \begin{tabular}{|l|c|c|c|c|c|c|} \hline Outcome Rolled & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline Number of Rolls & 30 & 50 & 39 & 30 & 29 & 22 \\ \hline \end{tabular}
Fill in the table below. Round your answers to the nearest thousandth. (a) Assuming that the cube is fair, compute the theoretical probability of rolling an even number. $\square$ (b) From Tammy's results, compute the experimental probability of rolling an even number. $\square$ (c) Assuming that the cube is fair, choose the statement below that is true: The largent number of rolls, the greater the likelihood that the experimental probability will be close to the theoretical probability. The smaller the number of rolls, the greater the likelihood that the experimental probability will be close to the theoretical probability. The experimental probability will never be very close to the theoretical probability, no matter the number of rolls. Explanation Check

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Problem 139

Espaniol
The spinner below shows 10 equally sized slices. Karen spun the dial 1000 times and got the following r \begin{tabular}{|c|c|c|c|} \hline Outcome & White & Grey & Black \\ \hline Number of Spins & 498 & 326 & 176 \\ \hline \end{tabular}
Fill in the table below. Round your answers to the nearest thousandth. (a) From Karen's results, compute the experimental probability of landing on grey or white. $\square$ (b) Assuming that the spinner is fair, compute the theoretical probability of landing on grey or white. $\square$ (c) Assuming that the spinner is fair, choose the statement below that is true: With a large number of spins, there must be no difference between the experimental and theoretical probabilities. With a large number of spins, there might be a difference between the experimental and theoretical probabilities, but the difference should be small.
With a large number of spins, there must be a large difference between the experimental and theoretical probablilities.

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Problem 140

The spinner below shows 5 equally sized slices. Mai spun the dial 500 times and got the following results. \begin{tabular}{|c|c|c|c|} \hline Outcome & Grey & White & Black \\ \hline Number of Spins & 297 & 101 & 102 \\ \hline \end{tabular}
Fill in the table below. Round your answers to the nearest thousandth. (a) From Mal's results, compute the experimental probability. of landing on grey or black. $\square$ (b) Assuming that the spinner is fair, compute the theoretical probability of landing on grey or black. $\square$ (c) Assuming that the spinner is fair, choose the statement below that is true: The larger the number of spins, the greater the likelihood that the experimental probability will be close to the theoretical probability. The experimental probability will never be very close to the theoretical probability, no matter the number of spins.
The smaller the number of spins, the greater the likelihood that the experimental probability will be close to the theoretical probability.

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Problem 141

Suppose the lifetime of EACH (blue, green or black) component follows an exponential distribution with mean 50 hours. (Be careful with your calculations.....any rounding can result in an incorrect answer...I suggest you use EXCEL for this question). Give all answers to FOUR decimal places. (i) What is the probability that a single component will last upto 45 hours? 0.5934 (ii) What is the probability that a single component will last longer than 45 hours? 0.4066 (iii) What is the probably that the first block (containing $\mathrm{C}_{1}, \mathrm{C}_{2}$ ) last longer than 45hours? 0.1653 (iv) What is the probability that the top and bottom branch together (containing $\mathrm{C}_{1} . \mathrm{C}_{2} . \mathrm{C}_{2}$ and $\mathrm{C}_{1}$ ) last longer than 45 hours? 0.3033 (v) What is the probability that the entire system will still be functioning after 45 hours? 0.0273

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Problem 142

Español
Keiko rolled a number cube 50 times and got the following results. \begin{tabular}{|c|c|c|c|c|c|c|} \hline Outcome Rolled & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline Number of Rolls & 10 & 5 & 10 & 10 & 5 & 10 \\ \hline \end{tabular}
Fill in the table below. Round your answers to the nearest thousandth. (a) Assuming that the cube is fair, compute the theoreticalprobability of rolling a 5 or 6 . (b) From Keiko's results, compute the experimental probability of rolling a 5 or 6 . $\square$ (c) Assuming that the cube is fair, choose the statement below that is true: The experimental and theoretical probabilities must always be equal. As the number of rolls increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal. As the number of rolls increases, we expect the experimental and theoretical probabilities to become farther apart.

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Problem 143

ii) $X=\{0,1,2,3,4,5\}$ ialah satu pemboleh ubah rawak diskret dengan kebarangkaliannya ditunjukkan seperti dalam jadual berikut. $X=\{0,1,2,3,4,5\}$ is a discrete random variable with its probabilities as shown in the following table. \begin{tabular}{|c|c|c|c|c|c|c|} \hline $X=r$ & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline $P(X=r)$ & $m$ & $m$ & $m-n$ & $2 m$ & $n$ & $n$ \\ \hline \end{tabular}
Jika $n=2 m$ , cari nilai $m$ dan nilai $n$ . If $n=2 m$ , find the value of $m$ and of $n$ . [3 markah / 3 marks]

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Problem 144

Name: Aufgabe 1: Aus einer Urne mit 6 nummerierten Kugeln (1bis 6 ) werden zwei Kugeln entnommen. Bestimmen Sie die Wahrscheinlichkeit dafür, dass eine Kugel mit der Nummer 4 und eine mit der Nummer 1 gezogen werden. 1.1 Sie werden nacheinander mit Zurücklegen entnommen. 1.2 Sie werden nacheinander ohne Zurücklegen mit Beachtung der Reihenfolge entnommen. 1.3 Sie werden mit einem Griff entnommen, ohne Beachtung der Reihenfolge.
In einem neuen Experiment sollen folgende Wahrscheinlichkeiten bestimmt werden: 1.4 Die Kugeln werden mit einem Griff entnommen. Wie groß ist die Wahrscheinlichkeit, dass beide Kugeln eine gerade Zahl anzeigen. 1.5 Wie groß ist die Wahrscheinlichkeit, dass die Augensumme größer als 10 ist?

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Problem 145

4. Interventionsstudie
Ein neues Medikament gegen Akne wird an einer Gruppe von 200 Personen ausprobiert. Eine Vergleichsgruppe von 80 Personen erhält ein Placebo. Bei 50 Personen der Interventionsgruppe wirkt das Medikament. In der Placebogruppe heilt die Krankheit bei 10 Personen ab. \begin{tabular}{|c|c|c|} \hline \multicolumn{3}{|c|}{H $\overline{\mathrm{H}}$ } \\ \hline M & 50 & 200 \\ \hline P & 10 & 80 \\ \hline & & \\ \hline \end{tabular} (M: Medikament, P: Placebo, H: Heilung, $\bar{H}$ : keine Heilung) a) Vervollständigen Sie die Vierfeldertafel. b) Vergleichen Sie die Erfolgswahrscheinlichkeit der Interventionsgruppe mit der Erfolgswahrscheinlichkeit der Placebogruppe. c) Bei Jakob heilt die Krankheit ab. Mit welcher Wahrscheinlichkeit hat er dennoch nur das Scheinmedikament erhalten?
5. Französisch
In einer Reisegruppe mit 30 Personen sprechen 16 Französisch. 60\% der Teilnehmer sind weiblich. 6 Mädchen sprechen Französisch. a) Stellen Sie eine Vierfeldertafel auf. b) Wie viele Jungen sprechen Französisch? c) Eines der Mädchen wird zur Sprecherin der Gruppe gewählt. Mit welcher Wahrscheinlichkeit spricht sie Französisch?
6. Safari An einer Safari nehmen 200 Personen teil. 60\% der Teilnehmer sind Touristen, der Rest besteht aus Einheimischen. 10 Einheimische haben keine Wasservorräte, 30 Touristen haben einen Wasservorrat. a) Stellen Sie eine Vierfeldertafel auf. b) Einer der Touristen verirt sich in der Wuste. Mit welcher Wahrscheinlichkeit hat er keinen Wasservorrat und muss verdursten? c) Eine Person bekommt kurz nach dem Aufbruch Angst. In einem Dorf kauft sie sich doch noch Wasser. Mit welcher Wahrscheinlichkeit handelt es sich um einen Einheimischen?
7. Großfamilie
Eine Großfamilie besteht aus Erwachsenen und Kindern. 200 Erwachsene und 100 Kindel spielen ein Instrument. Insgesamt 80 Kinder spielen kein Instrument. Die Wahrscheinlichkeit, dass ein zufällig ausgewählter Erwachsener ein Instrument spielt, beträgt 20\%. a) Aus wie vielen Personen besteht die Familie? Wie viele Kinder und wie viele Erwachsene gehören zur Familie? b) Auf dem Fest spielt ein zufâlig ausgewâhltes Familienmitglied die Eröffnungsmelodie. Mit welcher Wahrscheinlichkeit handelt es sich um ein Kind?
8. Laboruntersuchung
In einem Hygienelabor werden 100 Wischproben auf die Krankheitserreger $A$ und $B$ untersucht. a) Vervollständigen Sie die Vierfeldertafel, b) Beurteilen Sie anhand der Vierfeldertafel, ob die Erreger A und B unabhängig voneinander auftreten.

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Problem 146

A small ferry runs every half hour from one side of a large river to the other. The histogram of the probability distribution for the random variable $Y=$ money collected (in dollars) on a randomly selected ferry trip is shown here.
What is the shape of this histogram? The shape of the probability histogram is fairly uniform with a single peak at $\$ 25$ collected. The shape of the probability histogram is skewed to the left with a single peak at \ $25 collected. The shape of the probability histogram is fairly symmetric with a single peak at$ \ $25$ collected. The shape of the probability histogram is skewed to the right with a single peak at \ $25 collected. The shape of the probability histogram is approximately Normal with a single peak at$ \ $25$ collected.

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Problem 147

A drawer of office supplies contains: 3 yellow highlighters, 7 green highlighters, and 4 pink highlighters. A highlighter will be selected from the drawer, then replaced, and another highlighter will be selected from the drawer. What is the probabillty that the first oraw is a green highlighter and the second

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Problem 148

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From experience, an airline knows that only $80 \%$ of the passengers booked for a certain flight actually show up. If 8 passengers are randomly selected, find the probability that at most 6 of them show up.
Carry your intermediate computations to at least four decimal places, and round your answer to two decimal places. (If necessary, consult a list of formulas.) $\square$ Explanation Check Q2024 McGraw HIIILC. All Rights Reserved. Torms of Use I Pivacy Center I Upcoming Earnings Search

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Problem 149

The shape of the distribution of the time required to get an oil change at a 10 -minute oil-change facility is skewed right. However, records indicate that the mean time is 11.3 minutes, and the standard deviation is 3.9 minutes. Complete parts (a) through (c). (a) To compute probabilities regarding the sample mean using the normal model, what size sample would be required? A. The sample size needs to be less than or equal to 30 . B. The sample size needs to be greater than or equal to 30. C. The normal model cannot be used if the shape of the distribution is skewed right. D. Any sample size could be used.

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Problem 150

The shape of the distribution of the time required to get an oil change at a 10 -minute oil-change facility is skewed right. However, records indicate that the mean time is 11.3 minutes, and the standard deviation is 3.9 minutes. Complete parts (a) through (c). (b) What is the probability that a random sample of $n=40$ oil changes results in a sample mean time less than 10 minutes?
The probability is approximately $\square$ . (Round to four decimal places as needed.) (c) Suppose the manager agrees to pay each employee a $\$ 50$ bonus if they meet a certain goal. On a typical Saturday, the oil-change facility will perform 40 oil changes between 10 A.M. and 12 P.M. Treating this as a random sample, there would be a $10 \%$ chance of the mean oil-change time being at or below what value? This will be the goal established by the manager.
There is a 10\% chance of being at or below a mean oil-change time of $\square$ minutes. (Round to one decimal place as needed.)

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Problem 151

Suppose that you roll a fair, 6-sided die 10 times. What's the probability that you get at least one 6 ? $\square$ (Round to 4 decimal places. Leave your answer in decimal form.)

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Problem 152

The distribution of head circumference for full term newborn female infants is approximately normal with a mean of 33.8 cm and a standard deviation of 1.2 cm .
Determine the approximate percentage of full term newborn female infants with a head circumference less than 33 cm . Enter your answer using two decimal places

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Problem 153

Si $Z$ est une variable aléatoire normale standard, la valeur $z$ pour laquelle $P(Z \leq z)=0.2580$ est A. -0.6495 B. 0.6018 C. 0.6999 D. 0.3982
Si $X$ est une variable aléatoire exponentielle de paramètre $\lambda=2$ , alors $P(X \geq 1)$ est égale à A. 0.1353 B. 0.3935 C. 0.6065 D. 0.8647

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Problem 154

A bag contains 13 yellow tokens and 7 green tokens. Two tokens are drawn from the bag without replacement. $\qquad$ Probabtity win change on second dran Draw a tree diagram to represent this experiment.

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Problem 155

4. (5.4 Properties of Estimators) Two chips are drawn without replacement from an urn containing five chips that are numbered 1 through 5 . The average of the two numbers drawn is to be used as an estimator, $\hat{\theta}$ , for the true average (mean) of all of the chips which is $\theta=3$ . Calculate $P(|\hat{\theta}-3|>1.0)$ .

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Problem 156

5. (5.4 Properties of Estimators) A sample of size $n=15$ is drawn from a normal distribution where $\sigma=10$ but $\mu$ is unknown. If $\mu=20$ , then what is the probability that the estimator $\hat{\mu}=\overline{\mathrm{Y}}$ will lie between 19.0 and 21.0?

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Problem 157

0 of 1 point
If two 6 -sided dice are rolled, what is the probability that the total of the two dice is 11 ? Express the answer as a fraction. $P(\text { sum of two dice }=11)=$ $\square$

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Problem 158

Determine whether each statement describes a mean or a proportion. Explain your reasoning. 5) "A survey asked 1500 American citizens whether they had suffered from food poisoning in the past year. There were 227 survey participants who responded "Yes". Determine a 95\% confidence interval for the probability that a randomly-chosen American has suffered from food poisoning in the past year." 6) "In a sample of 100 members at a certain gym, these members exercised on average 4.2 hours per week with a standard deviation of 0.8 hours. Write a $99 \%$ confidence interval for the amount of exercise hours per week for members at this gym." 7) "A professor believes that the average cost of a textbook is $\$ 175$ . She samples 50 textbooks and determines the average price of those books to be $\$ 180$ with a standard deviation of $\$ 40$ . Test her hypothesis at a confidence level of $90 \%$ ."

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Problem 159

Suppose the random variable $x$ is best described by a normal distribution with $\mu=20$ and $\sigma=6.8$ . Find the $z$ -score that corresponds to each of the following $x$ values. $\begin{array}{l} \text { (a) } x=29 \\ z=1.32 \end{array}$ (b) $x=26$ $z=\square$ $\begin{array}{l} \text { (c) } x=15 \\ z=\square \end{array}$ (d) $x=10$ $z=-1.47$ (e) $x=12$ $z=\square$ (f) $x=14$ $z=\square$

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Problem 160

In a certain orchard, the number of apples (a) in a tree is normally distributed with a mean of 300 apples and a standard deviation of 30 apples. Find the probability that a given tree has between 240 and 300 apples.
Be sure to use the $68 \%-95 \%-99.7 \%$ rule and do not round.

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Problem 161

At a certain factory, weekly wages (w) are normally distributed with a mean of $\$ 400$ and a standard deviation of $\$ 50$ . Find the probability that a worker selected at random makes between \$350 and \$450.
Be sure to use the $68 \%-95 \%-99.7 \%$ rule and do not round.

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Problem 162

You roll a 6-sided die two times.
What is the probability of rolling a 5 and then rolling a number greater than $2 ?$ Simplify your answer and write it as a fraction or whole number. $\square$ Submit

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Problem 163

You pick a card at random, put it back, and then pick another card at random.
What is the probability of picking an even number and then picking a factor of 10 ? Simplify your answer and write it as a fraction or whole number. $\square$ Submit Next up

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Problem 164

In many games, rolling doubles has beneficial results. Three people are playing a board game in which two dice are rolled. a) Use a tree diagram to illustrate the probability distribution of the number of doubles in three rolls of two dice. b) Calculate the probability of each outcome in the sample space. c) What is the expected number of doubles in the three rolls?

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Problem 165

Dashboard
14 Multiple Choice 3.5 points Courses
$14 / 39$ Calendar
-11.4\%
$-12 \%$
$12 \%$ $11.4 \%$

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Problem 166

$\begin{array}{c} \text { P(hsuccesses })=n^{C} p^{n}(1-\rho)^{n-h} \\ n^{B}=\frac{n!}{(n-h)|h|} \end{array}$ ${ }_{7} C_{5}\left(\frac{1}{6}\right)^{2}\left(\frac{1}{6}\right)^{5}$ ${ }_{7} C_{5}\left(\frac{1}{6}\right)^{5}\left(\frac{5}{6}\right)^{2}$ ${ }_{7} \mathrm{C}_{2}\left(\frac{1}{6}\right)^{2}\left(\frac{5}{6}\right)^{5}$ ${ }_{7} C_{2}\left(\frac{2}{6}\right)^{2}\left(\frac{4}{6}\right)^{5}$

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Problem 167

A certain game involves tossing 3 fair coins, and it pays $9 \notin$ for 3 heads, $4 \notin$ for 2 heads, fand $2 \notin$ for 1 head. Is $4 \notin$ a fair price to pay to play this game? That is, does the $4 \phi$ cost to play make the game fair?
The $4 c$ cost to play $\square$ is not a fair price to pay because the expected winnings are $\square$ 4. (Type an integer or a fraction. Simplify your answer.)

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Problem 168

Ten thousand raffle tickets are sold. One first prize of $\$ 1000$ , two second prizes of $\$ 750$ , and three third prizes of $\$ 200$ each will be awarded, with all winners selected randomly. If you purchased one ticket, what are your expected gross winnings?
The expected gross winnings are $\square$ cents. (Round your answer to the nearest whole cent.)

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Problem 169

Dreams Recalled during One Week \begin{tabular}{|l|c|c|c|c|} \hline & None & 1 to 4 & 5 or more & Total \\ \hline Group X & 15 & 28 & 57 & 100 \\ \hline Group Y & 21 & 11 & 68 & 100 \\ \hline Total & 36 & 39 & 125 & 200 \\ \hline \end{tabular}
The data in the table above were produced by a sleep researcher studying the number of dreams people recall when asked to record their dreams for one week. Group X consisted of 100 people who observed early bedtimes, and Group Y consisted of 100 people who observed later bedtimes. If a person is chosen at random from those who recalled at least 1 dream, what is the probability that the person belonged to Group $\mathrm{Y}^{\prime}$ ? A) $\frac{68}{100}$ B) $\frac{79}{100}$ C) $\frac{79}{164}$ D) $\frac{164}{200}$

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Problem 170

Explain the meaning of the law of large numbers. Does this law say anything about what will happen in a single observation or experiment? Why or why not?
Explain the meaning of the law of large numbers. Choose the correct answer below A. As the experiment is done more and more times, the experimenter learns how to do the experiment better. Therefore the number of outcomes should start to match the theoretical probability. B. The theoretical probability is more accurate if it involves large numbers. C. As the experiment is done more and more times, the proportion of times that a certain outcome occurs should get closer to the theoretical probability that that outcome would occur. D. If an experiment is conducted 1000 times, the probability that a certain outcome occurs should become more predictable than if it was conducted 1500 times.

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Problem 171

Let $x$ be a continuous random variable that follows a normal distribution with a mean of 200 and a standard deviation of 25 . Find the value of $x$ so that the area under the normal curve to the right of $x$ is 0.7967 .
Round your answer to two decimal places. $x=$ $\square$

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Problem 172

14. If $o\left(E^{\prime}\right)=9: 11$ , find $p(E)$ .
15. Find the probability of choosing 7 winning spots in nine-spot keno.

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Problem 173

16. A pen manufacturer gets its pen cartridges from 2 suppliers. $58 \%$ of the cartridges come from supplier A and $2.25 \%$ of them are defective. $42 \%$ of the cartridges come from supplier B and $1.75 \%$ of them are defective. Answer the following questions: (a) Draw a tree diagram representing the problem. (b) Find the probability that a cartridge is defective and from supplier A. (c) Find the probability that a randomly chosen cartridge is not defective.

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Problem 174

According to the records of an electric company serving the Boston area, the mean electricity consumption during winter for all households is 1650 kilowatt-hours per month. Assume that the monthly electricity consumption during winter by all households in this area have a normal distribution with a mean of 1650 kilowatt-hours and a standard deviation of 320 kilowatt-hours. The company sent a notice to Bill Johnson informing him that about $75 \%$ of the households use less electricity per month than he does. What is Bill Johnson's monthly electricity consumption? Round your answer to the nearest integer. Bill Johnson's monthly electricity consumption is approximately $\square$ kWh. eTextbook and Media

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Problem 175

Save \& Exit Certity Lesson: 10.1 Introduction to Probability
Question 7 of 16, Step 1 of 1 5/16 Correct JAQUELINE HERNANDEZ
A sample of 400 adults found that 94 do not like cold weather. However, 108 of those studied said that they had interest in taking skiing lessons. Based on this sample, if an adult is chosen at random, what is the probability that he or she has no desire to take skiing lessons? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

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Problem 176

The number of ants per acre in the forest is normally distributed with mean 42,000 and standard deviation 12,404 . Let $X=$ number of ants in a randomly selected acre of the forest. Round all answers to 4 decimal places where possible. a. What is the distribution of X ? $\mathrm{X} \sim \mathrm{N}($ $\square$ , $\square$ ) b. Find the probability that a randomly selected acre in the forest has fewer than 52,236 ants. $\square$ c. Find the probability that a randomly selected acre has between 46,025 and 60,884 ants. $\square$ d. Find the first quartile. $\square$ ants (round your answer to a whole number)

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Problem 177

A recent survey showed that 93 full-time employees out of a sample of 400 did not use all of their vacation days last year. However, 118 of those studied expressed a desire for more vacation time. Based on this sample, if a full-time employee is chosen at random, what is the probability that he or she is content with the vacation allowance? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
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Problem 178

The mean height of an adult giraffe is 19 feet. Suppose that the distribution is normally distributed with standard deviation 1 feet. Let $X$ be the height of a randomly selected adult giraffe. Round all answers to 4 decimal places where possible. a. What is the distribution of X ? $\mathrm{X} \sim \mathrm{N}($ $\square$ , b. What is the median giraffe height? $\square$ ft . c. What is the Z-score for a giraffe that is 20.5 foot tall? $\square$ d. What is the probability that a randomly selected giraffe will be shorter than 18.4 feet tall? $\square$ e. What is the probability that a randomly selected giraffe will be between 18 and 18.5 feet tall? $\square$ f. The 70th percentile for the height of giraffes is $\square$ ft.

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Problem 179

registration records show that households in Elmville have 0 to 5 pets. Suppose that a household in Elmville is randomly selected. Let $X$ be the number of istered pets for that household. Here is the probability distribution of $X$ . \begin{tabular}{|c|c|c|c|c|c|c|} \hline alue $\boldsymbol{x}$ of $\boldsymbol{X}$ & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline $\boldsymbol{P}(X=x)$ & 0.13 & 0.22 & 0.23 & 0.18 & 0.14 & 0.10 \\ \hline \end{tabular} or parts (a) and (b) below, find the probability that the randomly selected household has the number of pets described. (a) Less than 3: $\square$ (b) No less than 3: $\square$ Save For Later Submit Ass

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Problem 180

The following table describes the contents of a bag that contains red, green, blue, pink, and white marbles. \begin{tabular}{|c|c|} \hline Color & Number of Marbles \\ \hline Red & 12 \\ \hline Green & 6 \\ \hline Blue & 10 \\ \hline Pink & 9 \\ \hline White & 30 \\ \hline \end{tabular}
If you select a single marble out of the bag, what is the probability that it is a color other than white or blue? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

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Problem 181

A coin flip determines who gets the ball first at the beginning of a football game, with the visiting team calling heads or tails. The captain of one particular team always calls heads. In the first four games as visitor of a season, find the probability that his team (a) Wins the toss one time. (b) Loses the toss four times. (c) Wins the toss more than once. (d) Loses the toss no more than three times. (e) Loses the toss at least twice.
Write your answers in exact, simplified form.
Part 1 of 5 (a) The probability that the team wins the toss one time is 0.25 .
Part 2 of 5 (b) The probability that the team loses the toss all four times is $\frac{1}{16}$ .
Part 3 of 5 (c) The probability that the team wins the toss more than once is $\square$ .
Part 4 of 5 (d) The probability that the team loses the toss no more than three times is $\frac{15}{16}$ .
Part 5 of 5 (e) The probability that the team loses the toss at least twice is $\frac{11}{16}$ .

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Problem 182

Use the following table to find the probability that a randomly chosen member of the Student Government Board is a freshman or lives in on-campus housing. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth. \begin{tabular}{|c|c|c|} \hline \multicolumn{3}{|c|}{ Students on the Student Government Board } \\ \hline Classification & On-Campus Housing & Off-Campus Housing \\ \hline Freshman & 3 & 0 \\ \hline Sophomore & 2 & 3 \\ \hline Junior & 1 & 1 \\ \hline Senior & 3 & 2 \\ \hline Graduate Student & 1 & 1 \\ \hline \end{tabular}

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Problem 183

To choose the order of bands for the finals of a Battle of the Bands competition, Freddy puts a penny, a nickel, a dime, a quarter, and a half-dollar into five separate envelopes and has one band choose an envelope. The second band then chooses from the remaining envelopes. Draw a tree diagram to determine the sample space and find the probabilities for the selections of the two bands in the finals. Express probabilities as simplified fractions.
Part 1 of 6 (a) The sample space contains 20 outcomes.
Part 2 of 6 (b) Find the probability that the amount of the first coin is more than the amount of the second coin.
The probability that the amount of the first coin is more than the amount of the second coin is $\frac{1}{2}$ .
Part: $2 / 6$
Part 3 of 6 (c) Find the probability that neither coin is a nickel.
The probability that neither coin is a nickel is $\square$

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Problem 184

At your local carnival, there is a game where 40 rubber duckies are floating in a kiddie tub, and they each have their bottoms painted one of three colors. 7 are painted pink, 15 are painted blue, and 18 are painted purple. If the player selects a duck with a pink bottom, they receive three pieces of candy. If they select blue, they receive two pieces of candy. And if they select purple, they receive one piece of candy. If the game is played 78 times, what are the minimum and maximum amounts of candy that could be handed out?
Answer Keypad Keyboard Shortcut $\square$
Activate Windows Go to Settings to activate Win

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Problem 185

Save \& Exit Certify Lesson: 10.6 Expected Value JAQUELINE HERNANDEZ Question 3 of 15, Step 1 of 1 2/15 Correct 2
At your local carnival, there is a game where 40 rubber duckies are floating in a kiddie tub, and they each have their bottoms painted one of three colors. 5 are painted pink, 17 are painted blue, and 18 are painted purple. If the player selects a duck with a pink bottom, they receive three pieces of candy. If they select blue, they receive two pieces of candy. And if they select purple, they receive one piece of candy. If the game is played 75 times, what are the minimum and maximum amounts of candy that could be handed out?

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Problem 186

A shoe company conducts a survey to determine the expected value of online sales for their new line of shoes coming out next fall. Based on past years, they have observed the following data on the probability of selling different types of shoes in the new line. The company expects that 3493 people will visit the website for their new line on launch day. Note that some of the online shoppers will not make a purchase. \begin{tabular}{|c|c|c|} \hline Shoe type & Price & Probability \\ \hline Sneakers & $\$ 93.99$ & $\frac{3}{25}$ \\ \hline High heels & $\$ 83.25$ & $\frac{1}{20}$ \\ \hline Sandals & $\$ 50.50$ & $\frac{1}{10}$ \\ \hline Loafers & $\$ 70.75$ & $\frac{4}{25}$ \\ \hline \end{tabular}
How much should the company expect its shoppers to spend on the website on launch day? Round your answer to the nearest cent, if necessary.

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Problem 187

If $X$ represents a random variable coming from a normal distribution with mean 3 and if $P(X>4.1)=0.23$ , then $P(3<X<4.1)=0.27$ . True False

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Problem 188

According to flightstats.com, American Airlines flights from Dallas to Chicago are on time $80 \%$ of the time. Suppose 25 flights are randomly selected, and the number of on-time flights is recorded. (a) Explain why this is a binomial experiment. (b) Determine the values of $n$ and $p$ . (c) Find and interpret the probability that exactly 15 flights are on time. (d) Find and interpret the probability that fewer than 15 flights are on time. (e) Find and interpret the probability that at least 15 flights are on time. (f) Find and interpret the probability that between 13 and 15 flights, inclusive, are on time. (c) Using the binomial distribution, the probability that exactly 15 flights are on time is $\square$ (Round to four decimal places as needed.) Interpret the probability. In 100 trials of this experiment, it is expected that about (Round to the nearest whole number as needed.) $\square$ will result in exactly 15 flights being on time. (d) Using the binomial distribution, the probability that fewer than 15 flights are on time is (Round to four decimal places as needed.) $\square$ Interpret the probability. In 100 trials of this experiment, it is expected that about $\square$ will result in fewer than 15 flights being on time. (Round to the nearest whole number as needed.)

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Problem 189

1. Statistical Literacy List three methods of assigning probabilities.
2. Statistical Literacy Suppose a weather app says that the probability of rain today is $30 \%$ . What is the complement of the event "rain today"? What is the probability of the complement? (3.) Statistical Literacy What is the probability of (a) an event $A$ that is certain to occur? (b) an event $B$ that is impossible?
4. Statistical Literacy What is the law of large numbers? If you were using the relative frequency of an event to estimate the probability of the event, would it be better to use 100 trials or 500 trials? Explain.

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Problem 190

14. Critical Thinking (a) Explain why -0.41 cannot be the probability of some event. (b) Explain why 1.21 cannot be the probability of some event. (c) Explain why $120 \%$ cannot be the probability of some event. (d) Can the number 0.56 be the probability of an event? Explain.
15. Probability Estimate: Wiggle Your Ears Can you wiggle your ears?
Use the students in your statistics class (or a group of friends) to estimate the percentage of people who can wiggle their ears. How can your result be thought of as an estimate for the probability that a person chosen at random can wiggle his or her ears? Comment: National statistics indicate that about $13 \%$ of Americans can wiggle their ears (Source: Bernice Kanner, Are You Normal?, St. Martin's Press, New York).
16. Probability Estimate: Raise One Eyebrow Can you raise one eyebrow at a time? Use the students in your statistics class (or a group of friends) to estimate the percentage of people who can raise one eyebrow at a time. How can your result be thought of as an estimate for the probability that a person chosen at random can raise one eyebrow at a time? Comment: National statistics indicate that about $30 \%$ of Americans can raise one eyebrow at a time (see source in Problem 15).
17. Myers-Briggs: Personality Types Isabel Briggs Myers was a pioneer in the study of personality types. The personality types are broadly defined according to four main preferences. Do married couples choose similar or different personality types in their mates? The following data give an indication (Source: I. B. Myers and M. H. McCaulley, A Guide to the Development and Use of the Myers-Briggs Type Indicators).
Similarities and Differences in a Random Sample of 375 Married Couples \begin{tabular}{lc} \hline Number of Similar Preferences & Number of Married Couples \\ \hline All four & 34 \\ Three & 131 \\ Two & 124 \\ One & 71 \\ None & 15 \\ \hline \end{tabular}
Suppose that a married couple is selected at random. (a) Use the data to estimate the probability that they will have $0,1,2,3$ , or 4 personality preferences in common. (b) Do the probabilities add up to 1? Why should they? What is the sample space in this problem?
18. General: Roll a Die (a) If you roll a single fair die and count the number of dots on top, what is the sample space of all possible outcomes? Are the outcomes equally likely? (b) Assign probabilities to the outcomes of the sample space of part (a). Do the probabilities add up to 1 ? Should they add up to 1? Explain. (c) What is the probability of getting a number less than 5 on a single throw? (d) What is the probability of getting 5 or 6 on a single throw?

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Problem 191

Agriculture: Cotton A botanist has developed a new hybrid cotton plant that can withstand insects better than other cotton plants. However, there is some concern about the germination of seeds from the new plant. To estimate the probability that a seed from the new plant will germinate, a random sample of 3000 seeds was planted in warm, moist soil. Of these seeds, 2430 germinated. (a) Use relative frequencies to estimate the probability that a seed will germi. nate. What is your estimate? (b) Use relative frequencies to estimate the probability that a seed will not germinate. What is your estimate? (c) Either a seed germinates or it does not. What is the sample space in this problem? Do the probabilities assigned to the sample space add up to 1 ? Should they add up to 1? Explain. (d) Are the outcomes in the sample space of part (c) equally likely?

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Problem 192

8) An office at the college reports there is a $70 \%$ chance of a student passing a certain professor's prealgebra class. Represent a student passing as a success. a) In a class of 25 students use the Binomial Probability Formula to find the probability that if 5 students are selected that exactly 3 pass. b) Determine the mean and standard deviation using the formulas on p234 of the text.

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Problem 193

12. Critical Thinking Consider the experiment of tossing a fair coin three times, For each coin, the possible outcomes are heads or tails. (a) List the equally likely events of the sample space for the three tosses. (b) What is the probability that all three coins come up heads? Notice that the complement of the event "three heads" is "at least one tail." Use this information to compute the probability that there will be at least one tail.
13. Critical Thinking On a single toss of a fair coin, the probability of heads is 0.5 and the probability of tails is 0.5 . If you toss a coin twice and get heads on the first toss, are you guaranteed to get tails on the second toss? Explain.

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Problem 194

There is a $50 \%$ chance of having a child that is either a boy or a girl. If a couple has three girls, what is the probability their 4th child will be another girl?

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Problem 195

Avicenna, an insurance company, offers five-year commercial property insurance policies to small businesses. If the holder of one of these policies experiences property damage in the next five years, the company must pay out $\$ 23,600$ to the policy holder. Executives at Avicenna are considering offering these policies for $\$ 791$ each. Suppose that for each holder of a policy there is a $3 \%$ chance they will experience property damage in the next five years and a $97 \%$ chance they will not.
If the executives at Avicenna know that they will sell many of these policies, should they expect to make or lose money from offering them? How much?
To answer, take into account the price of the policy and the expected value of the amount paid out to the holder. Avicenna can expect to make money from offering these policies. In the long run, they should expect to make $\square$ dollars on each policy sold. Avicenna can expect to lose money from offering these policies. In the long run, they should expect to lose $\square$ dollars on each policy sold. Avicenna should expect to neither make nor lose money from offering these policies.

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Problem 196

QUESTION 3 Figure 2 shows two representations of a cube: - A 2D figure (the net) that lays out all the faces of the cube flat on a surface. - A 3D cube that shows all its faces at once.
The faces of the cube are labelled with the numbers $3,4,5,6,7$ , and 8 , use figure 2 to answer the following probability questions: \begin{tabular}{|c|c|c|} \hline & 8 & \\ \hline 3 & 4 & 5 \\ \hline & 7 & \\ \hline & 6 & \\ \hline \end{tabular}
Figure 2: Two representations of a cube 3.1 Consider rolling the cube once. What are the possible outcomes (sample space) when you roll the cube once? (6) 3.2 If the cube is rolled once, what is the theoretical probability that it lands on the: 3.2.1 face labelled 4? $\qquad$ 3.2.2 face labelled with an even number. $\qquad$ 3.2.3 face labelled 1? $\qquad$ 3.3 What is the probability that the cube does not land on the face labelled 8 when rolled once?
Page 5 of 7 CONFIDENTIAL MIP2602 Oct/Nov 2024 3.4 Suppose you roll the cube 15 times. Record your results on the table below. \begin{tabular}{|l|l|l|l|l|} \hline & & & & \\ \hline & & & & \\ \hline & & & & \\ \hline & & & & \\ \hline \end{tabular}

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Problem 197

Probabilidad básica Instrucciones: Responda las preguntas siguientes. Escriba su respuesta como decimal redondeado al centésimo más próximo.
1. Se sabe que un envío de 500 monitores para computadora contiene 10 monitores con defectos. Si se elige un monitor al azar, ¿qué probabilidad existe de que ese monitor sea defectuoso?
2. Un club de una escuela superior tiene 10 miembros del último año y 8 miembros de tercer año. Si se elige un miembro al azar para el cargo de presidente, ¿cuál es la probabilidad de que esa persona NO sea uno de los miembros del último año?
3. En un juego, se retira un naipe de una baraja que contiene naipes de color rojo, verde y azul. Si se retira un naipe azul, el jugador puede avanzar a la casilla siguiente. La baraja contiene 100 naipes, de los cuales 30 son rojos, 15 son azules y 55 son verdes. Si un jugador retira un naipe al azar, ¿qué probabilidad existe de que ese jugador avance a la casilla siguiente?

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Problem 198

1. De un grupo de alumnos compuesto por 10 alumnos de tercer grado y 8 de cuarto grado, se seleccionarán a dos alumnos para ser líderes por un día. Si el primer alumno seleccionado es de cuarto grado, ¿cuál es la probabilidad de que el segundo alumno seleccionado sea de tercer grado?
2. En un hospital, sobre una plantilla de 10 médicos, 3 están de guardia el sábado, 4 el domingo y 2 los dos días. Si se selecciona al azar a uno de los médicos, ¿qué probabilidad existe de que ese médico esté de quardia un sábado o un domingo?

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Problem 199

2. En un hospital, sobre una plantilla de 10 médicos, 3 están de guardia el sábado, 4 el domingo y 2 los dos días. Si se selecciona al azar a uno de los médicos, ¿qué probabilidad existe de que ese médico esté de guardia un sábado o un domingo?

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Problem 200

920 matembtico
3. En una lata de bizcochos, hay 4 bizcochos de trocitos de chocolate y 3 de harina de avena. Si un nifo toma al azar 2 bizcochos, ¿cuál es la probabilidad de que los 2 bizcochos sean de trocitos de chocolate?
4. En un sorteo, se extraen de a dos por vez los nombres de los participantes, La primera persona favorecida gana un premio de $\$ 500$ y la segunda persona, un premio de $\$ 100$ . Los participantes del sorteo pueden ingresar su nombre una sola vez y se registraron 400 personas. Si ya se ha otorgado el primer premio, ¿qué probabilidad existe de ganar el segundo premio?
5. La tabla siguiente muestra datos de un estudio sobre 46 estudiantes de una escuela superior local. Cada número representa el total de estudiantes que pertenecen a esa categoría. \begin{tabular}{lll} & \begin{tabular}{l} Vive hasta $\mathbf{5}$ millas \\ de la escuela \end{tabular} & \begin{tabular}{l} Vive a más de $\mathbf{5}$ millas \\ de la escuela \end{tabular} \\ \hline \begin{tabular}{l} Planea ir a la \\ universidad \end{tabular} & 10 & 25 \\ \hline \begin{tabular}{l} No planea ir a la \\ universidad \end{tabular} & 8 & 3 \\ \hline \end{tabular}
Si se selecciona al azar a un estudiante, ¿cuál es la probabilidad de que este viva hasta 5 millas de la escuela y planee ir a la universidad?

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Probability

Problem 101

Problem 102

Problem 103

The density of XXX is given by f(x)={10/x2, for x>100, for x≤10f(x)=\left\{\begin{array}{ll} 10 / x^{2}, & \text { for } x>10 \\ 0, & \text { for } x \leq 10 \end{array}\right.f(x)={10/x2,0,​ for x>10 for x≤10​What is the distribution function of XXX ? Find P{X>20}P\{X>20\}P{X>20}.

Problem 104

Problem 105

2.2 Complete the following: 2.2.1 For exhaustive events: P(A\mathrm{P}(\mathrm{A}P(A or B)=…)=\ldots)=…. 2.2.2 For mutually exclusive events: P(A\mathrm{P}(\mathrm{A}P(A and B)=…)=\ldots)=….

Problem 106

Problem 107

Thee Probodility that a Sede Gered Gnt "1/3 if three of the eed planted. What, "s the proboblity to Nor-Germinaber at least Une wil gaminates Only One will Guminets

Problem 108

Problem 109

Problem 110

Problem 111

Problem 112

Problem 113

You pick a coin from the bag. Then, without replacing it, pick another coin. What is the probability QQQ of picking a quarter, then a nickel? Answer as a simplified fraction in the form a/b.

Problem 114

Problem 115

Problem 116

You pick a card at random. 4 5 6 7What is P(\mathrm{P}(P( less than 5))) ? Write your answer as a percentage. □\square□ \% Submit

Problem 117

Problem 118

Problem 119

Problem 120

Determine the probability of the given opposite event. What is the probability that a 50%50 \%50% free-throw shooter will miss her next free throw?The probability that a 50%50 \%50% freethrow shooter will miss her next free throw is (Type an integer or a decimal.) □\square□

Problem 121

Problem 122

Problem 123

Use the "at least once" rule to find the probability of the following event. Getting rain at least once in 4 days if the probability of rain on each single day is 0.2The probability is □\square□ (Round to three decimal places as needed.)

Problem 124

Problem 125

Problem 126

Problem 127

Problem 128

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Problem 134

Problem 135

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Problem 137

distribution below? 0.2 0.4 1 3

Problem 138

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Problem 141

Problem 142

Problem 143

Problem 144

Problem 145

Problem 146

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Problem 150

Problem 151

Suppose that you roll a fair, 6-sided die 10 times. What's the probability that you get at least one 6 ? □\square□ (Round to 4 decimal places. Leave your answer in decimal form.)

Problem 152

Problem 153

Problem 154

A bag contains 13 yellow tokens and 7 green tokens. Two tokens are drawn from the bag without replacement. \qquad Probabtity win change on second dran Draw a tree diagram to represent this experiment.

Problem 155

Problem 156

5. (5.4 Properties of Estimators) A sample of size n=15n=15n=15 is drawn from a normal distribution where σ=10\sigma=10σ=10 but μ\muμ is unknown. If μ=20\mu=20μ=20, then what is the probability that the estimator μ^=Y‾\hat{\mu}=\overline{\mathrm{Y}}μ^​=Y will lie between 19.0 and 21.0?

Problem 157

0 of 1 pointIf two 6 -sided dice are rolled, what is the probability that the total of the two dice is 11 ? Express the answer as a fraction. P( sum of two dice =11)=P(\text { sum of two dice }=11)=P( sum of two dice =11)= □\square□

Problem 158

Problem 159

Problem 160

Problem 161

Problem 162

You roll a 6-sided die two times.What is the probability of rolling a 5 and then rolling a number greater than 2?2 ?2? Simplify your answer and write it as a fraction or whole number. □\square□ Submit

Problem 163

You pick a card at random, put it back, and then pick another card at random.What is the probability of picking an even number and then picking a factor of 10 ? Simplify your answer and write it as a fraction or whole number. □\square□ Submit Next up

Problem 164

Problem 165

The density of $X$ is given by $f(x)=\left\{\begin{array}{ll} 10 / x^{2}, & \text { for } x>10 \\ 0, & \text { for } x \leq 10 \end{array}\right.$
What is the distribution function of $X$ ? Find $P\{X>20\}$ .

2.2 Complete the following: 2.2.1 For exhaustive events: $\mathrm{P}(\mathrm{A}$ or B $)=\ldots$ . 2.2.2 For mutually exclusive events: $\mathrm{P}(\mathrm{A}$ and B $)=\ldots$ .

You pick a coin from the bag. Then, without replacing it, pick another coin. What is the probability $Q$ of picking a quarter, then a nickel? Answer as a simplified fraction in the form a/b.

You pick a card at random. 4 5 6 7
What is $\mathrm{P}($ less than 5 $)$ ? Write your answer as a percentage. $\square$ \% Submit

Determine the probability of the given opposite event. What is the probability that a $50 \%$ free-throw shooter will miss her next free throw?
The probability that a $50 \%$ freethrow shooter will miss her next free throw is (Type an integer or a decimal.) $\square$

Use the "at least once" rule to find the probability of the following event. Getting rain at least once in 4 days if the probability of rain on each single day is 0.2
The probability is $\square$ (Round to three decimal places as needed.)

Suppose that you roll a fair, 6-sided die 10 times. What's the probability that you get at least one 6 ? $\square$ (Round to 4 decimal places. Leave your answer in decimal form.)

A bag contains 13 yellow tokens and 7 green tokens. Two tokens are drawn from the bag without replacement. $\qquad$ Probabtity win change on second dran Draw a tree diagram to represent this experiment.

5. (5.4 Properties of Estimators) A sample of size $n=15$ is drawn from a normal distribution where $\sigma=10$ but $\mu$ is unknown. If $\mu=20$ , then what is the probability that the estimator $\hat{\mu}=\overline{\mathrm{Y}}$ will lie between 19.0 and 21.0?

0 of 1 point
If two 6 -sided dice are rolled, what is the probability that the total of the two dice is 11 ? Express the answer as a fraction. $P(\text { sum of two dice }=11)=$ $\square$

You roll a 6-sided die two times.
What is the probability of rolling a 5 and then rolling a number greater than $2 ?$ Simplify your answer and write it as a fraction or whole number. $\square$ Submit

You pick a card at random, put it back, and then pick another card at random.
What is the probability of picking an even number and then picking a factor of 10 ? Simplify your answer and write it as a fraction or whole number. $\square$ Submit Next up

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14 Multiple Choice 3.5 points Courses
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$12 \%$ $11.4 \%$

Let $x$ be a continuous random variable that follows a normal distribution with a mean of 200 and a standard deviation of 25 . Find the value of $x$ so that the area under the normal curve to the right of $x$ is 0.7967 .
Round your answer to two decimal places. $x=$ $\square$

14. If $o\left(E^{\prime}\right)=9: 11$ , find $p(E)$ .
15. Find the probability of choosing 7 winning spots in nine-spot keno.