Probability

Problem 1201

A bag has 4 red and 7 white balls. If a ball is drawn and replaced with the other color, what is the probability the second is red?

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Problem 1202

An urn has 4 white, 6 black, and 8 red balls. What is the probability of drawing a black ball and then a white ball?

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Problem 1203

Part 2 of 2
A bowl contains blue and pink marbles. A scoop of marbles that is a representative sample contains 39 blue marbles and 26 pink marbles. a. Can you predict if there are more blue marbles or more pink marbles in the bowl? Explain. b. There are 750 marbles in a bowl. If you pick one marble from the bowl, are you more likely to pick a blue marble or a pink marble? a. Can you predict if there are more blue marbles or more pink marbles in the bowl? Explain. Choose the correct answer below. Yes. Because the representative sample contains more blue marbles than pink marbles, you can predict that the bowl contains more blue marbles than pink marbles. B. No. Because the sample is random, there is no way to predict what the bowl contains. C. No, because it is unknown whether the bowl contains other colored marbles D. Yes. Because the representative sample contains more pink marbles than blue marbles, you can predict that the bowl contains more pink marbles than blue marbles. b. There are 750 marbles in a bowl. If you pick one marble from the bowl, are you more likely to pick a blue marble or a pink marble?
If there are 750 marbles in the bow, then there are about $\square$ blue marbles and $\square$ pink marbles. So, you are $\square$ marble.

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Problem 1204

12. Devices Roughly $73 \%$ of Americans have a laptop/desktop computer, while only $45 \%$ have some sort of tablet. $36 \%$ of Americans are lucky enough to have both types of devices in their homes. What is the probability that a randomly selected home has a) a tablet, but no desktop/laptop? b) has either a tablet or a desktop/laptop? c) has neither computing device?

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Problem 1205

A $0.35 M$ solution of sucrose in water, and a beaker of pure water, both at $37 .{ }^{\circ} \mathrm{C}$ .
The solution is put into a semipermeable bag immersed in the water, and $50 . \mathrm{mL}$ of pure water flows through the bag into the sucrose solution. $\Delta S<0$ $\Delta S=0$ $\Delta S>0$ not enough information

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Problem 1206

(1 point) The daily demand $x$ for a certain product is a random variable with the probability density function $f(x) = \frac{6}{8}x(2-x)$ for $0 \le x \le 2$ .
Determine the expected value of demand: 1
Determine the standard deviation of demand: 0.447
Determine the probability that $x$ is within one standard deviation of the mean: 0.430

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Problem 1207

Suppose that $P(A)=0.50, P(B)=0.25$ , and the events $A$ and $B$ are disjoint events. Determine: a. the probability that event $A$ does not occur. b. the probability that event $A$ or $B$ occurs. c. the probability that neither event $A$ nor event $B$ occurs. d. the conditional probability that event $A$ occurs given that event B will occur. e. the conditional probability that event B will occur given that event $A$ will occur. f. whether or not events $A$ and $B$ are independent events.

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Problem 1208

$54 \%$ of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability that the number of U.S. adults who have very little confidence in newspapers is (a) exactly five, (b) at least six, and (c) less than four. (a) $P(5)=$ $\square$ (Round to three decimal places as needed.)

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Problem 1209

Decide which of the following statements are true.
Answer
There are an unlimited number of normal distributions.
The line of symmetry for all normal distributions is $x = 0$ .
The total area under a normal distribution curve equals $1$ .
The inflection points for any normal distribution are three standard deviations on either side of the mean.

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Problem 1210

$\text{Given that 477 out of 1722 people have a commute of more than 10 minutes, calculate the probability that a randomly selected person has a commute of more than 10 minutes. Round your answer to four decimal places.}$

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Problem 1211

If $X$ is a binomial random variable with $n$ trials and success probability $p$ , then as $n$ gets larger, the distribution of $X$ becomes (Choose one) skewed, less

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Problem 1212

Assume the variable $X$ is normally distributed with mean 120 and standard deviation 13. Find $P(100 < X < 155)$ NOTE: You must add an attachment to this question that shows all of your work in getting the answer to receive credit.

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Problem 1213

Use the Cumulative Normal Distribution Table to find the $z$ -score for which the area to its left is $0.69$ . The $z$ -score for the given area is

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Problem 1214

$x$ | $P(x)$ ---|--- 56 | 0.3 66 | 0.8 76 | 0.2 86 | -0.3 Determine whether the table represents a discrete probability distribution. Explain why The table (Choose one) represent Send data to Excel

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Problem 1215

Whether events are independent is not always obvious. Consider a set of basketball free throws by a single player Is the probability of success the same for each free throw? Justify your answer.

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Problem 1216

Suppose that the New England Colonials baseball team is equally likely to win any particular game as not to win it. Suppose also that we choose a random sample of 30 Colonials games.
Answer the following. (If necessary, consult a list of formulas.) (a) Estimate the number of games in the sample that the Colonials win by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response. $\square$ (b) Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your respons to at least three decimal places. $\square$

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Problem 1217

Determine whether the distribution represents a probability distribution.
$X$ | 3 | 7 | 10 $P(X)$ | 0.1 | 0.3 | -0.2
Send data to Excel
Part: 0 / 2
Part 1 of 2
The distribution (Choose one) a probability distribution. represents does not represent

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Problem 1218

Children's Obesity The following information shows the percentage of children who are obese for 3 age groups: \begin{tabular}{|c|c|} \hline Age & Percent \\ \hline $3-5$ & 6.6 \\ \hline $6-11$ & 15 \\ \hline $12-19$ & 22.5 \\ \hline \end{tabular}
If a child is selected at random, find each probability.
Part 1 of 2 (a) If you select a 12-19 year old child, the child is obese.
The probability is $22.5 \%$ .
Part: $1 / 2$
Part 2 of 2 (b) If you select a 12-19 year old child, the child is not obese.
The probability is $\square \%$ . 7028065

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Problem 1219

12. When four fair coins are tossed, what is the probability that the outcome will consist of two heads and two tails? (A) $\frac{1}{2}$ (B) $\frac{11}{20}$ (C) $\frac{1}{3}$ (D) $\frac{1}{4}$ (E) $\frac{3}{8}$

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Problem 1220

11. Amy has a bag containing 3 red, 2 blue and 1 white balls. She picks 2 balls from the bag and does not replace them a. What is the probability that the first ball is red? b. What is the probability that the two balls are red? c. What is the probability that either one of the balls is red? d. What is the probability that no white ball will be picked?

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Problem 1221

e Brady \& Matthew Camera Company has just come out with their newest professional Español ality digital camera, the ToughPix1. The company is selling this camera only through its w mobile app at a profit of $\$ 382$ per camera. This purchase comes with a guarantee that, rring gross negligence, if the camera breaks in the first two years after purchase, Brady \& atthew will replace it free of charge. Replacing a camera in this way costs the company $\$ 2300$ . ppose for each ToughPix1 there is a $5 \%$ chance that it will need to be replaced exactly once, $\%$ chance that it will need to be replaced exactly twice, and a $93 \%$ chance that it will not ed to be replaced. necessary, consult a list of formulas.) If Brady \& Matthew knows that it will sell many of these cameras, should it expect to make or lose money from selling them? How much?
To answer, take into account the profit earned on each camera and the expected value of the cost of replacements of the camera.

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Problem 1222

Karbis on 7 valget ja 2 musta küünalt. Leia tõenäosus:
a. mõlemad valged b. mõlemad mustad c. erinevat värvi d. üks punane e. ühte värvi.

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Problem 1223

Laual on 4 kahvlit ja 5 nuga. Jaan võtab 4 eset. Arvuta tõenäosus, et seal on vähemalt 2 kahvlit.

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Problem 1224

What is the probability that a randomly chosen patient was satisfied or had brain surgery? Round to 3 decimal places.

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Problem 1225

Calculate the probability of drawing 2 chocolates from a bag with 12 chocolates, 5 gums, and 4 taffies. Round to three decimals.

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Problem 1226

Find the percentage of values below $125$ in a normal distribution with mean $159$ and standard deviation $17$ .

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Problem 1227

A student ran out of time on a multiple choice exam and randomly guessed the answers for two problems. Each problem had 4 answer choices - $a$ , $b$ , $c$ , $d$ - and only one correct answer. What is the probability that she answered both of the problems correctly? Do not round your answer.

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Problem 1228

Find the probability that a random card (2, 3, or 4) is even or greater than 2. Give your answer as a percentage.

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Problem 1229

What is the probability of landing on a number greater than 6 or less than 7 when spinning a spinner with 5, 6, and 7?

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Problem 1230

Find the probability of drawing an even or prime card from a 52-card deck. Express your answer as a simplified fraction.

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Problem 1231

$n = 28$ , $p = 0.55$ Mean: $\mu =$ Variance: $\sigma^2 =$ Standard deviation: $\sigma =$ Part 3 of 4

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Problem 1232

A pizza shop sells three sizes of pizza, and they track how often each size gets ordered along with how much they profit from each size. Let $X$ represent the shop's profit on a randomly selected pizza. Here's the probability distribution of $X$ along with summary statistics:
| | Small | Medium | Large | | :-------- | :---- | :----- | :---- | | $X$ = profit (\$) | 4 | 8 | 12 | | $P(X)$ | 0.18 | 0.50 | 0.32 |
Mean: $\mu_X = \$8.56$ Standard deviation: $\sigma_X = \$2.77$
The company is going to run a promotion where customers get $\$2$ off any size pizza. Assume that the promotion will not change the probability that corresponds to each size. Let $Y$ represent their profit on a randomly selected pizza with this promotion.
What are the mean and standard deviation of $Y$ ?
$\mu_Y =$ ______ dollars $\sigma_Y =$ ______ dollars

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Problem 1233

3 Eine Schale enthält vier rote und drei blaue Kugeln. Es werden zufällig zwei Kugeln mit Zurück- legen entnommen. Mit welcher Wahrscheinlichkeit a) sind es zwei rote Kugeln, b) ist eine Kugel blau und eine rot, c) ist mindestens eine rote Kugel dabei, d) ist höchstens eine blaue Kugel dabei?

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Problem 1234

Which of the following are characteristics of a normal distribution? The normal distribution curve crosses the $x$ axis. The normal distribution curve is symmetric about the standard deviation. The total area under the normal distribution curve is 1.00 .
The area under the part of a normal curve that lies within 3 standard deviations of the mean is approximately 0.95 . The area under the part of a normal curve that lies within 1 standard deviation of the mean is approximately 0.68 . The normal distribution curve is unimodal. A normal distribution curve is bell shaped. The mean, median, and mode are located at the center of the distribution. The normal curve is a discrete distribution.
The area under the part of a normal curve that lies within 2 standard deviations of the mean is approximately 0.95 . Check

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Problem 1235

Assume that a procedure yields a binomial distribution with a trial repeated $n=30$ times. Use the binomial probability formula to find the probability of $x=5$ successes given the probability $p='15$ of success on a single trial. Round to three decimal places.

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Problem 1236

Role model vs. Ievel of education \begin{tabular}{lccc} & Family member & Friend or acquaintance & Stranger \\ \hline Less than high school & 0.09 & 0.12 & 0.19 \\ High school & 0.25 & 0.32 & 0.40 \\ Some college & 0.29 & 0.25 & 0.23 \\ Bachelor's degree & 0.23 & 0.19 & 0.14 \\ Advanced degree & 0.14 & 0.12 & 0.04 \\ Column total & 1.00 & 1.00 & 1.00 \end{tabular}
Based on the data, which of the following statements must be true of the people surveyed?
Choose 1 answer: (A) A person whose role model is a family member is less likely to have an advanced deffree than a person whose role model is a friend or acquaintance. (B) A person whose role model is a stranger is more likely to have high school than some college as their highest level of education. (C) A person whose highest level of education is a bachelor's degree is more likely to have a family member than a stranger as a role model. (D) A person whose highest level of education is less than high school is more likely to have a stranger than a friend or acquaintance as a role model.

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Problem 1237

5.12: Let the random variable $Y_n$ have distribution that is $b(n, p)$ a) Prove that $\frac{X_n}{n}$ converges in probability to $p$ . This result is one form of the weak law of large numbers. b) Prove that $1 - \frac{X_n}{n}$ converges in probability to $1 - p$ c) Prove that $(\frac{X_n}{n})(1 - \frac{Y_n}{n})$ converges in probability to $p(1 - p)$ let $z_n =$ $= \lim_{n \to \infty} p(|z|$

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Problem 1238

5.12: Let the random variable $Y_n$ have distribution that is $b(n, p)$ a) Prove that $\frac{X_n}{n}$ converges in probability to $p$ . This result is one form of the weak law of large numbers. b) Prove that $1 - \frac{X_n}{n}$ converges in probability to $1 - p$ c) Prove that $(\frac{X_n}{n})(1 - \frac{Y_n}{n})$ converges in probability to $p(1 - p)$

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Problem 1239

The weights of badgermoles in the Earth Kingdom are normally distributed, with mean weight 1150 kg and standard deviation 50 kg . Find the probability that a badgermole caught at random has a weight greater than 1260 kg . z Table Link 0.0122 0.0162 0.0158 0.0150

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Problem 1240

Suppose a drawer contains four green socks, five red socks, and three white socks. We draw one sock from the drawer and it is equally likely that any one of the socks is drawn. Find the probabilities of the events in parts (a)-(e).
a. Find the probability that the sock is red. (Type an integer or a simplified fraction.)
b. Find the probability that the sock is green or white. (Type an integer or a simplified fraction.)
c. Find the probability that the sock is brown. (Type an integer or a simplified fraction.)
d. Find the probability that the sock is not green. (Type an integer or a simplified fraction.)
e. We reach into the drawer without looking to pull out four socks. What is the probability that we get at least two socks of the same color? (Type an integer or a simplified fraction.)

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Problem 1241

A report asked people who got their news from television which television sector they relied on primarily for their news: local TV, network TV, or cable TV. The results were used to generate the data in the table below. Determine whether being female is independent of choice of local TV. Explain your answer in the context of this problem. \begin{tabular}{|c|c|c|c|c|} \hline & Local TV & Network TV & Cable TV & Total \\ \hline Men & 67 & 49 & 55 & \\ \hline Women & 85 & 55 & 56 & \\ \hline Total & & & & \\ \hline \end{tabular}
Since $\square$ $=$ $\square$ \% and $\square$ $=$ $\square$ $\%$ , the events $\square$ independent. (Type integers or decimals rounded to one decimal place as needed.)

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Problem 1242

A recent poll asked respondents to fill in the blank to this question: "The country $\qquad$ when it comes to giving equal rights to women" with one of three choices. The results are shown in the accompanying table using a sample size of 80 men and 80 women. Complete parts a and b below. \begin{tabular}{|l|c|c|c|c|} \hline & \begin{tabular}{c} Hasn't Gone \\ Far Enough \end{tabular} & \begin{tabular}{c} Has Been \\ About Right \end{tabular} & \begin{tabular}{c} Has Gone \\ Too Far \end{tabular} & Total \\ \hline Men & 33 & 35 & 12 & 80 \\ \hline Women & 43 & 29 & 8 & 80 \\ \hline Total & 76 & 64 & 20 & 160 \\ \hline \end{tabular} A. P(male and responded "hasn't gone far enough") B. P(hasn't gone far enough | male) C. $P$ (male I hasn't gone far enough) b. Find the probability that a person randomly selected from only the men in this group responded "hasn't gone far enough."
The probability is $\square$ (Simplify your answer.)

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Problem 1243

Lottery machine outputs digits 0-9 in 200 trials. Find: (a) experimental probability of even numbers, (b) theoretical probability, (c) true statement about trials and probabilities. Round answers to nearest thousandths.

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Problem 1244

Mary rolled a cube 40 times. Find the experimental probability of rolling a 4, the theoretical probability, and a true statement.

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Problem 1245

A spinner has 3 yellow, 1 red, and 1 blue slice. After 1000 spins, Jane got 606 yellow, 181 red, 213 blue.
(a) Find the experimental probability of yellow or red. (b) Find the theoretical probability of yellow or red. (c) True statement about experimental vs theoretical probability with more spins?

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Problem 1246

According to a study on teenage shopping behavior, it was found that $75\%$ of female teens regularly shop in stores rather than shopping online. If a group of 6 female teenagers are selected at random, what is the probability that at least 3 of them regularly do their shopping in stores? (Round your answer to four decimal places.)

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Problem 1247

Let $y$ denote the number of broken eggs in a randomly selected carton of one dozen eggs. \begin{tabular}{|c|c|c|c|c|c|} \hline $y$ & 0 & 1 & 2 & 3 & 4 \\ \hline $p(y)$ & 0.60 & 0.25 & 0.10 & 0.03 & 0.02 \\ \hline \end{tabular} (a) Calculate and interpret $\mu_{y}$ . $\mu_{y}=$ $\square$ (b) Consider the following questions. (i) In the long run, for what percentage of cartons is the number of broken eggs less than $\mu_{y}$ ? $\qquad$ \% (ii) Does this surprise you? Yes No (c) Explain why $\mu_{y}$ is not equal to $\frac{0+1+2+3+4}{5}=2.0$ . This computation of the mean is incorrect because it does not take into account that the number of broken eggs are all equally likely. This computation of the mean is incorrect because the value in the denominator should equal the maximum $y$ value. This computation of the mean is incorrect because it does not take into account the number of partially broken eggs. This computation of the mean is incorrect because it includes zero in the numerator which should not be taken into account when calculating the mean. This computation of the mean is incorrect because it does not take into account the probabilities with which the number of broken eggs need to be weighted.

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Problem 1248

1 2 $=3$ $\checkmark 4$ 6 7 5 8 9 10
High Blood Pressure Twenty-one percent of Americans ages 25 to 74 have high blood pressure. If 16 randomly selected Americans ages 25 to 74 are selected, find each probability. Round your answers to at least 3 decimal places.
Part 1 of 3 (a) None will have high blood pressure. $P($ none have high blood pressure $)=0.025$
Part 2 of 3 (b) One-half will have high blood pressure. $P$ (one-half have high blood pressure) $=0.007$
Part: $2 / 3$
Part 3 of 3 (c) Exactly 7 will have high blood pressure. $P($ exactly 7 have high blood pressure $)=$ $\square$

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Problem 1249

Question 5
A survey of athletes at a high school is conducted, and the following facts are discovered: $40 \%$ of the athletes are football players, $22 \%$ are basketball players, and $15 \%$ of the athletes play both football and basketball. An athlete is chosen at random from the high school: what is the probability that the athlete is either a football player or a basketball player?
Probability = $\square$ \% (Please enter your answer as a percent)

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Problem 1250

Question 6
In a large population, $55 \%$ of the people have been vaccinated. If 5 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated?
Give your answer as a decimal to 4 places.

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Problem 1251

Giving a test to a group of students, the grades and gender are summarized below Grades and Gender \begin{tabular}{|c|r|r|r|r|} \hline & \multicolumn{1}{|c|}{ A } & B & C & Total \\ \hline Male & 19 & 10 & 18 & $\mathbf{4 7}$ \\ \hline Female & 2 & 3 & 9 & $\mathbf{1 4}$ \\ \hline Total & $\mathbf{2 1}$ & $\mathbf{1 3}$ & $\mathbf{2 7}$ & $\mathbf{6 1}$ \\ \hline \end{tabular}
If one student is chosen at random, find the probability that the student was female AND got a "C". Round your answer to 4 decimal places. $\square$

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Problem 1252

A card is drawn from a well-shuffled deck of 52 cards. Find the probability of drawing a black 2.
The probability is $\boxed{}$ . (Simplify your answer. Type an integer or a fraction.)

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Problem 1253

\begin{tabular}{cccc} & Bachelor's & Master's & Doctorate \\ Men & 653,037 & 313,838 & 25,771 \\ Women & 687,564 & 315,906 & 25,253 \end{tabular}
Send data to Excel
Choose a degree at random. Find the probabilities of the following. Express your answer as a fraction or a decimal rounded to three decimal places.
Part 1 of 4 (a) What is the probability that the degree is a bachelor's degree? $P(\text { bachelor's degree })=0.663$
Part 2 of 4 (b) What is the probability that the degree was a master's degree or a degree awarded to a women? $P(\text { master's degree or awarded to woman })=0.664$
Part: 2 / 4
Part 3 of 4 (c) What is the probability that the degree was a bachelor's degree awarded to a men. $P(\text { bachelor's degree awarded to men })=$ $\square$ Skip Part Check Save For Later Submit Assianm

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Problem 1254

Question 14 of 25 (1 point) | Question Attempt: 1 or I
College Degrees Awarded The table below represents the college degrees awarded in a recent academic year by Español gender. \begin{tabular}{cccc} & Bachelor's & Master's & Doctorate \\ \hline Men & 548,254 & 251,468 & 23,728 \\ Women & 609,872 & 270,538 & 23,320 \end{tabular} Send data to Excel
Choose a degree at random. Find the probabilities of the following. Express your answer as a fraction or a decimal rounded to three decimal places.
Part: $0 / 4$ $\square$
Part 1 of 4 (a) What is the probability that the degree is a doctorate? $P(\text { doctorate })=0.027$ $\square$
Part: $1 / 4$ $\square$
Part 2 of 4 (b) What is the probability that the degree was a bachelor's degree or a degree awarded to a men? $P(\text { bachelor's degree or awarded to men })=$ $\square$ Next Part

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Problem 1255

Compound Probability Score: 3/4 Penalty: none
Question Watch Video Show Examples A bag contains 6 red marbles, 7 blue marbles and 4 green marbles. If two marbles are drawn out of the bag, what is the probability, to the nearest 10ooth, that both marbles drawn will be green?

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Problem 1256

From historical data, $18 \%$ of people work out daily $(p=0.18)$ . In a sample of 15 $(n=15)$ people, use the binomial formula or your TI-8314 to determine the probability that exactly 4 (of the fifteen) work out daily.
For a standard normal distribution: a) What is the probability that $z$ is less than 0.47 ? b) What is the probability that $z$ is greater than -1.83 ? $\qquad$ c) What is the probability that $z$ is between -1.29 and 0.64 ? $\qquad$ d) What is the probability that $z$ is between -1.96 and 1.96 ? $\qquad$

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Problem 1257

An aptitude test is designed to measure leadership abilities of the test subjects. Suppose that the scores on the test are normally distributed with a mean of 570 and a standard deviation of 120. The individuals who exceed 700 on this test are considered to be potential leaders. What proportion of the population are considered to be potential leaders? Round your answer to at least four decimal places. $\square$

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Problem 1258

Determine the probability of the given complementary event. What is the probability of randomly selecting a month of the year and not getting a month that contains the letter $g$ ?
The probability is $\square$ (Type an integer or a simplified fraction.)

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Problem 1259

The following table shows the distribution of murders by type of weapon for murder cases in a particular country over the past 12 years. Complete Weapon parts (a) through (e).
Weapon | Probability ------- | -------- Handgun | 0.479 Rifle | 0.026 Shotgun | 0.033 Unknown firearm | 0.148 Knives | 0.135 Hands, fists, etc. | 0.054 Other | 0.125
(a) Is the given table a probability model? Why or why not? A. No; the probability of all events in the table is not greater than or equal to 0 and less than or equal to 1, and the sum of the probabilities of all outcomes does not equal 1. B. No; the sum of the probabilities of all outcomes does not equal 1. C. No; the probability of all events in the table is not greater than or equal to 0 and less than or equal to 1. D. Yes; the rules required for a probability model are both met.
(b) What is the probability that a randomly selected murder resulted from a rifle or shotgun? $P(\text{rifle or shotgun}) =$ (Type a decimal rounded to three decimal places as needed.)

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Problem 1260

11 (2 pts.) Create the sample space of possible outcomes of landing on heads or tails from tossing a dime, nickel and a quarter simultaneously.

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Problem 1261

12 (4 pts.) Of 50 iPads available for checkout at the library, 10 are defective. A sample of 3 iPads are randomly selected without replacement. What is the probability that at least one of the iPads is defective? Round to the nearest thousandth. Show your work.

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Problem 1262

Homework: HW \#7: Sections 6.1-6.3 Question 9, 6.1.21-T HW Score: $16.67 \%, 8$ of 48 points Part 1 of 2 Points: 0 of 1 Save
Question list Question 9 Question 10 Question 11 Question 12 Question 13 Question 14
Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1 . Draw a graph and find the probability of a bone density test score greater than 0.59 . $\qquad$ Sketch the region. Choose the correct graph below. A. B. c.
D. Help me solve this View an example Get more help - Clear all Check answer Dec 9 2:36 US

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Problem 1263

She repeats this several times. The table shows her results.
Based on her results, what is the probability of choosing an orange marble from the bag?
Color Frequency Green 5 Orange 11 Purple 4
Color Probability Green $\frac{1}{4}$ Orange

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Problem 1264

Natalie saw these animals: deer (6), raccoon (7), coyote (3), bobcat (3), mountain lion (2). Estimate coyotes in next 50.

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Problem 1265

Estimate how many of the next 100 groups will choose the Grouchy Goblins room, given 9 out of 50 chose it last week.

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Problem 1266

Find the probability that independent events $K$ and $J$ occur, given $P(K)=0.40$ and $P(J)=0.20$ .

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Problem 1267

What are the odds of a perfect bracket if a user predicts $66.7\%$ of games correctly? A. 1 in 120.2 billion B. 1 in 66.7 C. 1 in 1,202 D. 1 in 120

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Problem 1268

What is the probability $\mathrm{P}$ of selecting a card that is not a birthday card from 21 total cards, 14 of which are birthday cards? Round to 2 decimal places.

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Problem 1269

In Virginia, $15\%$ of households use energy-saving bulbs. Of those, $15\%$ use only energy-saving bulbs. Find the expression for exclusive users: A) $0.00225 h$ B) $0.0225 h$ C) $0.225 h$ D) $2.25 h$

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Problem 1270

Find the area under the standard normal distribution curve to the right of $z = 0.37$ . Use the Standard Normal Distribution Table and enter the answer to 4 decimal places. The area to the right of the z value is

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Problem 1271

Find the area under the standard normal distribution curve between $z = -2.72$ and $z = 0.16$ . Use The Standard Normal Distribution Table and enter the answer to 4 decimal places. The area between the two z values is ______.

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Problem 1272

Written Response - 5 marks Royalty Chocolates advertises that it sells bags of chocolates with at least 40 chocolates in each bag. A large sample of bags are opened and the number of chocolates is counted. The results are normally distributed with a mean of 43.5 chocolates and a standard deviation of 1.4 chocolates. Calculate the $z$ -score for a data value of 40.

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Problem 1273

P8-11 Integrative: Expected return, standard deviation, and coefficient of variation Three assets-F, G, and H-are currently under consideration by Perth Industries. The probability distributions of expected returns for these assets are shown in the following table. \begin{tabular}{|c|c|c|c|c|c|c|} \hline \multirow[b]{2}{*}{i} & \multicolumn{2}{|r|}{Asset F} & \multicolumn{2}{|r|}{Asset G} & \multicolumn{2}{|r|}{Asset H} \\ \hline & $P_{r_{i}}$ & Return, $r_{i}$ & $P_{r_{i}}$ & Return, $r_{i}$ & Pri & Return, $r_{i}$ \\ \hline 1 & 0.10 & 40\% & 0.40 & 35\% & 0.10 & 40\% \\ \hline 2 & 0.20 & 10 & 0.30 & 10 & 0.20 & 20 \\ \hline 3 & 0.40 & 0 & 0.30 & $-20$ & 0.40 & 10 \\ \hline 4 & 0.20 & $-5$ & & & 0.20 & 0 \\ \hline 5 & 0.10 & -10 & & & 0.10 & $-20$ \\ \hline \end{tabular} a. Calculate the average return, $\bar{r}$ , for each of the three assets. Which provides the largest average return? b. Calculate the standard deviation, $\sigma_{n}$ , for each asset's returns. Which appears to have the greatest risk? c. Calculate the coefficient of variation, CV, for each asset's returns. Which appears to have the greatest relative risk?

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Problem 1274

3.
Yukarıda verilen kartlar ters çevrilip karıştrilıyor ve hafiza oyunu oynanıyor. Hafıza oyununda ilk kartı kuğu olarak açan Duru'nun ikinci kartta kuğuyu açma olasııığı aşağıdakilerden hangisidir? A) $\frac{1}{7}$ B) $\frac{2}{7}$ C) $\frac{3}{7}$ D) $\frac{1}{2}$

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Problem 1275

KAAF Graduate Students Survey talked to 1000 students ages 18-35 about personal finance. The survey found that 33% of the students have their own credit card.
a. In a sample of six (6) students, what is the probability that two (2) will have their own credit card? [8 marks]
b. In a sample of six (6) students, what is the probability that at least two (2) will have their own credit card? [7 marks]

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Problem 1276

A company has 10 employees, and the manager wants to randomly select 3 employees to attend a training workshop. The employees are listed as follows:
1. Alice
2. Bob
3. Charlie
4. David
5. Emma
6. Frank
7. Grace
8. Helen
9. Ian
10. Jack
KAFC 613: Quantitative Methods | End of Sem. Exams - 2024 | S.B. Egala (PhD) 2
a. How many different possible samples of 3 employees can be selected from this population? [6 marks] b. If each sample has an equal chance of being selected, what is the probability of selecting the sample {Alice, Bob, Charlie}? [9 marks]

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Problem 1277

3. For the following probability distribution, find $P(2 \leq X<5)$ \begin{tabular}{|l|l|l|l|l|l|l|} \hline $X$ & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline $f(x)$ & 0.03 & 0.14 & & 0.33 & 0.15 & 0.04 \\ \hline \end{tabular}
4. If Z is the standard normal distribution, find the probability that Z lies between $\mathbf{- 2 . 6 8}$ and 0.
5. Assume that the weight loss for the first month of a diet is normally distributed with a mean of 3.6 Kgs and a standard deviation of 0.6 Kgs . Find the probability of at least 5 Kgs weight lost.
6. Suppose that $X$ is normally distributed with a mean of 90 and a standard deviation of 10 , find a value $x$ such that $P(X>x)=0.815$ .

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Problem 1278

6. In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.
A box contains five identical balls numbered 1 to 5 respectively. One ball is chosen at random from the box. Its number is recorded and the ball is replaced in the box.
This process was carried out 75 times in total.
How many times would you expect an even-numbered ball to have been chosen? You must show all your working. $3 + 200$

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Problem 1279

Five males with an X-linked genetic disorder have one child each. The random variable $x$ is the number of children among the five who inherit the X-linked genetic disorder. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied.
$x$ | $P(x)$ ---|--- 0 | 0.027 1 | 0.153 2 | 0.320 3 | 0.320 4 | 0.153 5 | 0.027
Does the table show a probability distribution? Select all that apply. A. Yes, the table shows a probability distribution. B. No, the random variable $x$ 's number values are not associated with probabilities. C. No, the random variable $x$ is categorical instead of numerical. D. No, not every probability is between 0 and 1 inclusive. E. No, the sum of all the probabilities is not equal to 1.
Find the mean of the random variable $x$ . Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $\mu =$ child(ren) (Round to one decimal place as needed.) B. The table does not show a probability distribution.
Find the standard deviation of the random variable $x$ . Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $\sigma =$ child(ren) (Round to one decimal place as needed.) B. The table does not show a probability distribution.

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Problem 1280

Fernando has 40 movies at home. Of these movies, 14 are comedy, 6 are documentaries, and 20 are adventure. Spanish is the language of $\frac{1}{2}$ of the comedy movies and $\frac{1}{4}$ of the adventure movies.
Based on this information, which statement is true?
F The probability of randomly selecting a comedy movie in Spanish is 50%. G The probability of randomly selecting a comedy movie in Spanish is less than the probability of randomly selecting a documentary. H The probability of randomly selecting a movie that is in Spanish is 30%. J The probability of randomly selecting an adventure movie in Spanish is greater than the probability of randomly selecting a comedy movie in Spanish.

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Problem 1281

Find the indicated $z$ score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.
The indicated $z$ score is $\boxed{\phantom{0.00}}$ . (Round to two decimal places as needed.)
0 $z$ 0.2090

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Problem 1282

Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean $0$ and standard deviation $1$ .
The area of the shaded region is $\boxed{}$ . (Round to four decimal places as needed.)
$z = -0.88$

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Problem 1283

(04.01 LC) In Denver, Colorado there is a 10% probability of snow on a specific day. How was this probability most likely determined? On days with similar conditions as this day, it has snowed 10% of the time in Denver, Colorado. On this day each year, it snowed 10% of the time. On days with similar conditions as this day, it has snowed 10% of the time in Colorado. During this month, it snowed 10% of the days. The probability was determined randomly.

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Problem 1284

5. The rate of cat births each day of the year for feral cats in Belton are normally distributed. The average is 4.8 births a day, with the standard deviation being .70 births a day. Approximately what percentage of days have between 3.4 and 5.5 cat births?

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Problem 1285

An urn contains 6 green and 8 pink balls. Five balls are randomly drawn from the urn in succession, with replacement. That is, after each draw, the selected ball is returned to the urn. What is the probability that all 5 balls drawn from the urn are green? Round your answer to three decimal places. (If necessary, consult a list of formulas.) $\square$

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Problem 1286

5. Tomoka places her favorite recipes in a recipe book. She has 5 chicken dishes, 4 fish dishes, 3 soups, and 8 desserts. If Tomoka picks 2 distinct recipes at random from the book, what is the probability that she selects a chicken dish and a dessert (in any order)?

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Problem 1287

Use the graph, showing the results of a survey of the hours of sleep a group of Americans gets each night, to determine the truth value of each simple statement in the following compound statement. Then determine the truth value of the compound statement. Four percent of Americans get 4 or fewer hours of sleep each night or $32 \%$ get 8 or more hours of sleep each night, and $30 \%$ get 6 or more hours of sleep each night.
The truth value of the simple statement "Four percent of Americans get 4 or fewer hours of sleep each night" is

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Problem 1288

Find the expected value $(\mu)$ and standard deviation $(\sigma)$ for the distribution of $X$ with given probabilities. Options: $\mu=4.44, \sigma=1.93$ , $\mu=4.44, \sigma=3.73$ , $\mu=2.22, \sigma=3.73$ , $\mu=2.22, \sigma=1.93$ .

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Problem 1289

Find the expected value $(\mu)$ and standard deviation $(\sigma)$ for the distribution of $X$ with given probabilities.

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Problem 1290

What percent of students must be vaccinated for herd immunity against pertussis with an RO of 18? Options: $50 \%$ , $25 \%$ , $100 \%$ , $5 \%$ , $90 \%$ , $10 \%$ , $95 \%$ , $75 \%$ .

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Problem 1291

What is the probability of rolling a sum of 3 with two 12-sided dice in 5 out of 10 trials?

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Problem 1292

13. Elena sta giocando a tombola ed estrae un numero dal sacchetto (i numeri vanno da 1 a 90 ). Qual è la probabilità che il Massimo Comune Divisore tra il numero estratto ed il numero 42 risulti maggiore di 10 ? (A) $1 / 15$ (B) $1 / 10$ (C) $7 / 90$ (D) $1 / 9$ (E) $4 / 45$

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Problem 1293

Learn with an example or Watch a video $X$ is a normally distributed random variable with mean 69 and standard deviation 7. What is the probability that $X$ is between 49 and $89 ?$ Write your answer as a decimal rounded to the nearest thousandth. $\square$ Submit

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Problem 1294

Higrment $\# 2$
Throe cans are tessoed. What are the values of rondom varrable $z$ reppesenting the mumbers of tails?

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Problem 1295

A die is rolled. Find the probability of the given event. (a) The number showing is a 4 ;
The probability is : (b) The number shoning is an even number;
The probability is : $\square$ (c) The number showing is greater than 2 ;
The probability is : $\square$ Question Help: Video

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Problem 1296

A bag contains 8 red marbles, 9 yellow marbles, and 7 green marbles. How many additional red marbles must be added to the 24 marbles already in the bag so that the probability of randomly drawing a red marble is $\frac{3}{5}$ ?
A. 11 B. 16 C. 20 D. 24 E. 32

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Problem 1297

Find the indicated probability. Express your answer as a simplified fraction unless otherwise noted. 6) The table below shows the soft drinks preferences of people in three age groups. \begin{tabular}{r|ccc} & cola & root beer & lemon-lime \\ \hline under 21 years of age & 40 & 25 & 20 \\ between 21 and 40 & 35 & 20 & 30 \\ over 40 years of age & 20 & 30 & 35 \end{tabular}
If one of the 255 subjects is randomly selected, find the probability that the person drinks root beer given that they are over 40 . A) $\frac{2}{5}$ B) $\frac{2}{17}$ C) $\frac{6}{17}$ D) None of the above is correct.

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Problem 1298

```latex \text{The number of telephone calls that arrive at a phone exchange is often modeled as a Poisson random variable. Assume that on the average there are 4 calls per 141 minutes. What is the probability of no calls in 1.157 hour?}
\text{NOTE: give your answer to 6 decimal places.} ```

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Problem 1299

$\text{1) Berechnen Sie den Erwartungswert und die Standardabweichung für die Zufallsgröße } X, \text{ die die nebenstehende Wahrscheinlichkeitsverteilung hat:}$
$\begin{array}{c|c} x & P(X = x) \\ \hline -1 & \frac{1}{5} \\ 0 & 0 \\ 1 & a \\ 2 & \frac{2}{5} \\ \end{array}$
$\text{Hinweis: Die Summe der Wahrscheinlichkeiten muss 1 ergeben, also } \frac{1}{5} + 0 + a + \frac{2}{5} = 1.$

See Solution

Problem 1300

```latex \text{In einem Beutel liegen zwei 1-Cent- und zwei 2-Cent-Münzen. Jana zieht zwei Münzen ohne Zurücklegen.}
\begin{enumerate} \item[A)] \text{Geben Sie drei Zufallsgrößen an, die man bei diesem Experiment beobachten kann.} \item[B)] \text{Berechnen Sie Erwartungswert und Standardabweichung dieser Zufallsgrößen.} \end{enumerate} ```

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1 ...10 11 12 13 14 15 16

Probability

Problem 1201

A bag has 4 red and 7 white balls. If a ball is drawn and replaced with the other color, what is the probability the second is red?

Problem 1202

An urn has 4 white, 6 black, and 8 red balls. What is the probability of drawing a black ball and then a white ball?

Problem 1203

Problem 1204

Problem 1205

Problem 1206

Problem 1207

Problem 1208

Problem 1209

Problem 1210

Problem 1211

If XXX is a binomial random variable with nnn trials and success probability ppp, then as nnn gets larger, the distribution of XXX becomes (Choose one) skewed, less

Problem 1212

Assume the variable XXX is normally distributed with mean 120 and standard deviation 13. Find P(100<X<155)P(100 < X < 155)P(100<X<155) NOTE: You must add an attachment to this question that shows all of your work in getting the answer to receive credit.

Problem 1213

Use the Cumulative Normal Distribution Table to find the zzz-score for which the area to its left is 0.690.690.69. The zzz-score for the given area is

Problem 1214

xxx | P(x)P(x)P(x) ---|--- 56 | 0.3 66 | 0.8 76 | 0.2 86 | -0.3 Determine whether the table represents a discrete probability distribution. Explain why The table (Choose one) represent Send data to Excel

Problem 1215

Whether events are independent is not always obvious. Consider a set of basketball free throws by a single player Is the probability of success the same for each free throw? Justify your answer.

Problem 1216

Problem 1217

Determine whether the distribution represents a probability distribution.XXX | 3 | 7 | 10 P(X)P(X)P(X) | 0.1 | 0.3 | -0.2Send data to ExcelPart: 0 / 2Part 1 of 2The distribution (Choose one) a probability distribution. represents does not represent

Problem 1218

Problem 1219

12. When four fair coins are tossed, what is the probability that the outcome will consist of two heads and two tails? (A) 12\frac{1}{2}21​ (B) 1120\frac{11}{20}2011​ (C) 13\frac{1}{3}31​ (D) 14\frac{1}{4}41​ (E) 38\frac{3}{8}83​

Problem 1220

Problem 1221

Problem 1222

Karbis on 7 valget ja 2 musta küünalt. Leia tõenäosus:a. mõlemad valged b. mõlemad mustad c. erinevat värvi d. üks punane e. ühte värvi.

Problem 1223

Laual on 4 kahvlit ja 5 nuga. Jaan võtab 4 eset. Arvuta tõenäosus, et seal on vähemalt 2 kahvlit.

Problem 1224

What is the probability that a randomly chosen patient was satisfied or had brain surgery? Round to 3 decimal places.

Problem 1225

Calculate the probability of drawing 2 chocolates from a bag with 12 chocolates, 5 gums, and 4 taffies. Round to three decimals.

Problem 1226

Find the percentage of values below 125125125 in a normal distribution with mean 159159159 and standard deviation 171717.

Problem 1227

A student ran out of time on a multiple choice exam and randomly guessed the answers for two problems. Each problem had 4 answer choices - aaa, bbb, ccc, ddd - and only one correct answer. What is the probability that she answered both of the problems correctly? Do not round your answer.

Problem 1228

Find the probability that a random card (2, 3, or 4) is even or greater than 2. Give your answer as a percentage.

Problem 1229

What is the probability of landing on a number greater than 6 or less than 7 when spinning a spinner with 5, 6, and 7?

Problem 1230

Find the probability of drawing an even or prime card from a 52-card deck. Express your answer as a simplified fraction.

Problem 1231

n=28n = 28n=28, p=0.55p = 0.55p=0.55 Mean: μ=\mu = μ= Variance: σ2=\sigma^2 = σ2= Standard deviation: σ=\sigma = σ= Part 3 of 4

Problem 1232

Problem 1233

3 Eine Schale enthält vier rote und drei blaue Kugeln. Es werden zufällig zwei Kugeln mit Zurück- legen entnommen. Mit welcher Wahrscheinlichkeit a) sind es zwei rote Kugeln, b) ist eine Kugel blau und eine rot, c) ist mindestens eine rote Kugel dabei, d) ist höchstens eine blaue Kugel dabei?

Problem 1234

Problem 1235

Assume that a procedure yields a binomial distribution with a trial repeated n=30n=30n=30 times. Use the binomial probability formula to find the probability of x=5x=5x=5 successes given the probability p=′15p='15p=′15 of success on a single trial. Round to three decimal places.

Problem 1236

Problem 1237

Problem 1238

Problem 1239

The weights of badgermoles in the Earth Kingdom are normally distributed, with mean weight 1150 kg and standard deviation 50 kg . Find the probability that a badgermole caught at random has a weight greater than 1260 kg . z Table Link 0.0122 0.0162 0.0158 0.0150

Problem 1240

Problem 1241

Problem 1242

Problem 1243

Lottery machine outputs digits 0-9 in 200 trials. Find: (a) experimental probability of even numbers, (b) theoretical probability, (c) true statement about trials and probabilities. Round answers to nearest thousandths.

Problem 1244

Mary rolled a cube 40 times. Find the experimental probability of rolling a 4, the theoretical probability, and a true statement.

Problem 1245

A spinner has 3 yellow, 1 red, and 1 blue slice. After 1000 spins, Jane got 606 yellow, 181 red, 213 blue. (a) Find the experimental probability of yellow or red. (b) Find the theoretical probability of yellow or red. (c) True statement about experimental vs theoretical probability with more spins?

Problem 1246

Problem 1247

Problem 1248

Problem 1249

Problem 1250

Question 6In a large population, 55%55 \%55% of the people have been vaccinated. If 5 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated?Give your answer as a decimal to 4 places.

Problem 1251

Problem 1252

A card is drawn from a well-shuffled deck of 52 cards. Find the probability of drawing a black 2.The probability is \boxed{}​. (Simplify your answer. Type an integer or a fraction.)

If $X$ is a binomial random variable with $n$ trials and success probability $p$ , then as $n$ gets larger, the distribution of $X$ becomes (Choose one) skewed, less

Assume the variable $X$ is normally distributed with mean 120 and standard deviation 13. Find $P(100 < X < 155)$ NOTE: You must add an attachment to this question that shows all of your work in getting the answer to receive credit.

Use the Cumulative Normal Distribution Table to find the $z$ -score for which the area to its left is $0.69$ . The $z$ -score for the given area is

$x$ | $P(x)$ ---|--- 56 | 0.3 66 | 0.8 76 | 0.2 86 | -0.3 Determine whether the table represents a discrete probability distribution. Explain why The table (Choose one) represent Send data to Excel

Determine whether the distribution represents a probability distribution.
$X$ | 3 | 7 | 10 $P(X)$ | 0.1 | 0.3 | -0.2
Send data to Excel
Part: 0 / 2
Part 1 of 2
The distribution (Choose one) a probability distribution. represents does not represent

12. When four fair coins are tossed, what is the probability that the outcome will consist of two heads and two tails? (A) $\frac{1}{2}$ (B) $\frac{11}{20}$ (C) $\frac{1}{3}$ (D) $\frac{1}{4}$ (E) $\frac{3}{8}$

Karbis on 7 valget ja 2 musta küünalt. Leia tõenäosus:
a. mõlemad valged b. mõlemad mustad c. erinevat värvi d. üks punane e. ühte värvi.

Find the percentage of values below $125$ in a normal distribution with mean $159$ and standard deviation $17$ .

A student ran out of time on a multiple choice exam and randomly guessed the answers for two problems. Each problem had 4 answer choices - $a$ , $b$ , $c$ , $d$ - and only one correct answer. What is the probability that she answered both of the problems correctly? Do not round your answer.

$n = 28$ , $p = 0.55$ Mean: $\mu =$ Variance: $\sigma^2 =$ Standard deviation: $\sigma =$ Part 3 of 4

Assume that a procedure yields a binomial distribution with a trial repeated $n=30$ times. Use the binomial probability formula to find the probability of $x=5$ successes given the probability $p='15$ of success on a single trial. Round to three decimal places.

A spinner has 3 yellow, 1 red, and 1 blue slice. After 1000 spins, Jane got 606 yellow, 181 red, 213 blue.
(a) Find the experimental probability of yellow or red. (b) Find the theoretical probability of yellow or red. (c) True statement about experimental vs theoretical probability with more spins?

Question 6
In a large population, $55 \%$ of the people have been vaccinated. If 5 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated?
Give your answer as a decimal to 4 places.

A card is drawn from a well-shuffled deck of 52 cards. Find the probability of drawing a black 2.
The probability is $\boxed{}$ . (Simplify your answer. Type an integer or a fraction.)

Compound Probability Score: 3/4 Penalty: none
Question Watch Video Show Examples A bag contains 6 red marbles, 7 blue marbles and 4 green marbles. If two marbles are drawn out of the bag, what is the probability, to the nearest 10ooth, that both marbles drawn will be green?

Determine the probability of the given complementary event. What is the probability of randomly selecting a month of the year and not getting a month that contains the letter $g$ ?
The probability is $\square$ (Type an integer or a simplified fraction.)

She repeats this several times. The table shows her results.
Based on her results, what is the probability of choosing an orange marble from the bag?
Color Frequency Green 5 Orange 11 Purple 4
Color Probability Green $\frac{1}{4}$ Orange

Find the probability that independent events $K$ and $J$ occur, given $P(K)=0.40$ and $P(J)=0.20$ .

What are the odds of a perfect bracket if a user predicts $66.7\%$ of games correctly? A. 1 in 120.2 billion B. 1 in 66.7 C. 1 in 1,202 D. 1 in 120

What is the probability $\mathrm{P}$ of selecting a card that is not a birthday card from 21 total cards, 14 of which are birthday cards? Round to 2 decimal places.

In Virginia, $15\%$ of households use energy-saving bulbs. Of those, $15\%$ use only energy-saving bulbs. Find the expression for exclusive users: A) $0.00225 h$ B) $0.0225 h$ C) $0.225 h$ D) $2.25 h$

Find the area under the standard normal distribution curve to the right of $z = 0.37$ . Use the Standard Normal Distribution Table and enter the answer to 4 decimal places. The area to the right of the z value is

Find the area under the standard normal distribution curve between $z = -2.72$ and $z = 0.16$ . Use The Standard Normal Distribution Table and enter the answer to 4 decimal places. The area between the two z values is ______.