Probability

Problem 201

Bookwork code: 2B Calculator allowed
Charlotte spun a spinner a total of 200 times and worked out the estimated probability of it landing on green after different numbers of spins. Her results are shown in the table below. a) What is the best estimate for the probability of landing on green? Give your answer as a fraction in its simplest form. b) Copy and complete the sentence below, using one of the options to explain why your answer to part a) is the best estimate. \begin{tabular}{|c|c|c|c|c|c|} \hline Number of spins & 5 & 10 & 20 & 100 & 200 \\ \hline Estimated probability & $\frac{1}{5}$ & $\frac{1}{5}$ & $\frac{1}{4}$ & $\frac{19}{100}$ & $\frac{11}{50}$ \\ \hline \end{tabular} b) This is the best estimate because it $\qquad$ involves the smallest number of trials is the largest involves the largest number of trials is the mean Previous Watch video Answer

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Problem 202

Based on a poll, among adults who regret getting tattoos, $12 \%$ say that they were too young when they got their tattoos. Assume that five adults who regret getting tattoos are randomly selected, and find the indicated probability. Complete parts (a) through (d) below. a. Find the probability that none of the selected adults say that they were too young to get tattoos. 0.5277 (Round to four decimal places as needed.) b. Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos. 0.3598 (Round to four decimal places as needed.) c. Find the probability that the number of selected adults saying they were too young is 0 or 1 . $\square$ (Round to four decimal places as needed.)

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Problem 203

The table shows the probability distribution for a discrete random variable $X$ . a. Complete the table by finding the missing values of $x \cdot P(x)$ . Then compute the mean of the probability distribution. \begin{tabular}{|r|r|r|} \hline $x$ & $P(x)$ & $x \cdot P(x)$ \\ \hline 3 & 0.19 & \\ \hline 4 & 0.2 & 0.8 \\ \hline 5 & 0.37 & \\ \hline 6 & 0.24 & 1.44 \\ \hline \end{tabular} $\mu_{X}=4.66$

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Problem 204

Points: 0 of 1 Save
A survey showed that $34 \%$ of human resource professionals are at companies that rejected job candidates because of information found on their social media. If 26 human resource professionals are randomly selected, would 15 be a significantly high number to be at companies that rejected job candidates because of information found on their social media? Why or why not?
Select the correct choice below and fill in the answer box within your choice. (Round to four decimal places as needed.) A.
No, 15 would not be significantly high because the probability of 15 or more is $\square$ , which is low. B. No, 15 would not be significantly high because the probability of 15 or more is $\square$ , which is not low. c. Yes, 15 would be significantly high because the probability of 15 or more is $\square$ , which is not low. D. Yes, 15 would be significantly high because the probability of 15 or more is $\square$ , which is low.

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Problem 205

Assume that when human resource managers are randomly selected, $48 \%$ say job applicants should follow up within two weeks. If 25 human resource managers are randomly selected, find the probability that exactly 17 of them say job applicants should follow up within two weeks.
The probability is $\square$ (Round to four decimal places as needed.)

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Problem 206

Find the $z$ -score that has $67.4 \%$ of the distribution's area to its right.
The z -score is $\square$ 0.07 (Round to two decimal places as needed.)

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Problem 207

A consumer agency randomly selected 1700 flights from two major airlines, $A$ and $B$ . The Alowing table gives the classification of these flights based on their arrival time: \begin{tabular}{|l|c|c|c|c|} \hline Airline & $<30 \mathrm{~min}$ late & $30-60 \mathrm{~min}$ late & More 60 min late & \multicolumn{1}{|l|}{ Total } \\ \hline Airline A & 429 & 390 & { $[92$ } & 911 \\ \hline Airline B & 393 & 316 & 80 & { $[789$ } \\ \hline Total & 822 & 706 & 172 & 1700 \\ \hline \end{tabular} a) If a flight is selected at random, what is the probability that it is a flight from airline $A$ and more than 60 minutes late?

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Problem 208

The table summarizes the distribution of color and shape for 100 tiles of equal area. \begin{tabular}{|c|c|c|c|c|} \hline & Red & Blue & Yellow & Total \\ \hline Square & 10 & 20 & 25 & 55 \\ \hline Pentagon & 20 & 10 & 15 & 45 \\ \hline Total & 30 & 30 & 40 & 100 \\ \hline \end{tabular}
If one of these tiles is selected at random, what is the probability of selecting a red tile? (Express your answer as a decimal or fraction, not as a percent.)

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Problem 209

Given that Kieran saw exactly one of these types of animal, what is the probability that he saw a lion? Give your answer as a fraction in its simplest form.
Zoam Previous
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Problem 210

$82 \%$ $65 \%$ $35 \%$ $18 \%$

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Problem 211

Assume a coin is tossed three times. Compute the probability of tails and 2 heats me OOO 118 318 813 Desf Next Page

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Problem 212

The students at Roseville Academy look forward to the annual jog-a-thon every year. After students finish running their laps, they get their choice of ice pop. So far, of the 14 students who finished their jog-a-thon laps, 3 chose an orange ice pop, 5 chose lime, and 6 chose strawberry.
Based on the data, estimate how many of the remaining 78 students will choose a lime ice pop.
If necessary, round your answer to the nearest whole number. $\square$ students

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Problem 213

Since Maddie has a hard time picking out what to wear to school, she made a spinner to help her decide. The spinner is divided into 5 unequal sections labeled pants, skirt, dress, shorts, and overalls. She spun the spinner several times to make sure it was working. Here are her results: dress, pants, overalls, pants, skirt, dress, shorts, dress, overalls, skirt Based on the data, estimate how many times Maddie will wear a dress to school in the next 20 days.
If necessary, round your answer to the nearest whole number. $\square$ times

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Problem 214

Lacey volunteers in the lunchroom once a week and hands out drinks to the students who buy lunch. So far today, 9 students chose orange juice, 8 chose milk, and 13 chose water.
Based on the data, what is the probability that the next student will choose milk? Write your answer as a fraction or whole number. $\square$

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Problem 215

Thanks to the first big snowfall of the season, Winter Basin Snow Park is busy. Hassan is working the front counter of the rental booth. The table below shows the types of equipment he has rented out so far today. \begin{tabular}{|l|c|} \hline Type of equipment & Number rented \\ \hline snow tubes & 8 \\ \hline sleds & 15 \\ \hline saucers & 11 \\ \hline snowshoes & 2 \\ \hline \end{tabular}
Based on the data, what is the probability that Hassan's next customer will rent a saucer? Write your answer as a fraction or whole number.

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Problem 216

Let $T_{1}$ be the time between a car accident and reporting a claim to the insurance company. Let $T_{2}$ be the time between the report of the claim and payment of the claim. The joint density function of $T_{1}$ and $T_{2}, f\left(t_{1}, t_{2}\right)$ , is constant over the region $0<t_{1}<6,0<t_{2}<6, t_{1}+t_{2}<10$ , and zero otherwise.
Calculate $\mathrm{E}\left(T_{1}+T_{2}\right)$ , the expected time between a car accident and payment of the claim. A. 6.0 B. 5.7 c. 5.0 D. 4.9 E. 6.7

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Problem 217

Assume that $x$ has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) 〔 USE SALT $\begin{aligned} \mu & =106 ; \sigma=20 \\ P(x \geq 90) & = \end{aligned}$

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Problem 218

6. [0/1 Points]
DETAILS MY NOTES BBUNDERSTAT12HS 6.3.011.MI. PREVIOUS AN
Assume that $x$ has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) $\mu=28 ; \sigma=3.8$ $P(x \geq 30)=$ $\square$ Need Help? Read It Watch it Master It

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Problem 219

What value of $z$ divides the standard normal distribution so that half the area is on one side and half is on the other? Round your answer to two decimal places.

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Problem 220

2. Sophia tests 25 pens. Five of the pens do not write the first time. Sophia says the experimental probability that a pen will not write the first time is 0.2 . Is Sophia correct? Why? a. No, because you cannot predict whether the next pen will write or not b. No, because $\frac{20}{25}$ is 0.8 c. Yes, because $\frac{20}{25}$ is 0.2 d.) Yes, because $\frac{5}{25}$ is 0.2

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Problem 221

etting Chrome as default Set as default Module Knowlsdge Chack Question 5
Suppose that $55 \%$ of all babies born in a particular hospital are boys. If 6 babies born in the hospital are randomly selected, what is the probability that fewer than 2 of them are boys?
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.) $\square$

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Problem 222

5. The odds against a new car needing major repairs in the next few years are 24 to 1. What is the probability that the car will need major repairs in the next few years?

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Problem 223

A stationary store has decided to accept a large shipment of ball-point pens if an inspection of 16 randomly selected pens yields no more than two defective pens. ■ USE SALT (a) Find the probability that this shipment is accepted if $5 \%$ of the total shipment is defective. (Round your answer to three decimal places.) 0.953 (b) Find the probability that this shipment is not accepted if $15 \%$ of the total shipment is defective. (Round your answer to three decimal places.) 0.220

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Problem 224

\text{The Medical College Admissions Test (MCAT) consists of four sections:} \\ \text{- Chemical and Physical Foundations of Biological Systems (Chem/Phys)} \\ \text{- Critical Analysis and Reasoning Skills (CARS)} \\ \text{- Biological and Biochemical Foundations of Living Systems (Bio/BioChem)} \\ \text{- Psychological, Social, and Biological Foundations of Behavior (Psych/Soc)} \\
\text{The score for each section is approximately normal with a mean of 125 and standard deviation of 3. Assume the correlation between any two sections is 0.5. While a passing score on any section is generally considered to be 128, medical schools accept students (i.e., passed the exam) based on their total score on the MCAT, or a 512 score. For applicants interested in research positions, the Chem/Phys and Bio/BioChem sections are often referenced as most critical. For applicants interested in practicing medicine, the CARS and Psych/Soc sections are most critical.} \\
\text{Consider five random applicants to the same medical school where three of the applicants are interested in research and the other two are interested in practicing medicine. What is the expected total number of these applicants who pass their respective sections on the MCAT on their first attempt? [NOTE: While the MCAT itself and the sections are accurate, the numbers and decision rules were adjusted for this exam question.]} \\
\text{The user took a picture with their phone and the text was extracted above. The user then had a dialogue with an AI Assistant to help clarify the instructions.} \\
\text{Dialogue Transcript:} \\
\text{Hi there! It looks like we have a problem related to the MCAT exam scores. However, I need a bit more information before I can help you solve it. Specifically, I need to know:} \\
\text{1. Are we considering the expected number of applicants passing all their respective sections based on an individual section score requirement of 128, or are we considering the total score requirement of 512?} \\ \text{2. How are we expected to calculate or interpret the correlation between sections? Is it influencing the probability of passing?} \\
\text{Once I have this information, we can proceed and find the expected number of applicants passing their respective sections on their first attempt. Please provide these details, and we'll get started right away!} \\ \text{Disregard the 512 part} \\

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Problem 225

According to Harper's Index, $60 \%$ of all federal inmates are serving time for drug dealing. A random sample of 15 federal inmates is selected. USE SALT (a) What is the probability that 13 or more are serving time for drug dealing? (Round your answer to three decimal places.) (b) What is the probability that 2 or fewer are serving time for drug dealing? (Round your answer to three decimal places.) (c) What is the expected number of inmates serving time for drug dealing?

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Problem 226

A not-so-clever employee decided to fake his monthly expense report. He believed that the first digits of his expense amounts should be equally likely to be any of the numbers from 1 to 9 . In that case, the first digit $Y$ of a randomly selected expense amount would have the probability distribution shown in the histogram.
What proportion of first digits in the employee's expense amounts should be greater than $6 ?$ 0.333 0.444 0.667 0.25 0.389
Incorrect Answer

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Problem 227

Points: 0 of 1
Find the probability of $z$ occurring in the indicated region of the standard normal distribution. Click here to view page 1 of the standard normal table Click here to view page 2 of the standard normal table. $P(0<z<197)=\square$ (Round to four decimal places as needed.)

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Problem 228

Need Help? Read It Watch it Submit Answer 13. [4/5 Points] DETAILS MY NOTES BBUNDERSTAT12HS 5.R.019. PREVIOUS
An experiment consists of tossing an unfair coin. ( $40 \%$ chance of landing on heads) a specified number of times and recording the outcomes. (a) What is the pabability that the first head will occur on the second trial? (Use 4 decimal places.)

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Problem 229

changed each time it is given. Let $n=1,2,3, \ldots$ represent the number of times a person takes the CPA exam until the first pass. (Assume the trials are independent.) (a) What is the probability that Cathy passes the CPA on the first try? (Use 2 decimal places.) (b) What is the probability that Cathy passes the CPA exam on the second or third try? (Use 4 decimal places.) Need Help? Read it Submit Answer
15. [-/1 Points] DETAILS MY NOTES BBUNDERSTAT12HS 6.R.001. ASK YOUR TEACHER

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Problem 230

Practice Exercises 1) Which of the following are valid probability distributions? Explain a) \begin{tabular}{|c|c|} \hline $\boldsymbol{x}$ & $\boldsymbol{P}(\boldsymbol{x})$ \\ \hline 0 & 0.5 \\ \hline 1 & 0.25 \\ \hline 2 & 0.25 \\ \hline \end{tabular} b) \begin{tabular}{|c|c|} \hline $\boldsymbol{x}$ & $\boldsymbol{P}(\boldsymbol{x})$ \\ \hline 0.5 & 0.2 \\ \hline 0.2 & 0.3 \\ \hline 0.3 & 0.25 \\ \hline \end{tabular} c) \begin{tabular}{|c|c|} \hline $\boldsymbol{x}$ & $\boldsymbol{P}(\boldsymbol{x})$ \\ \hline 0 & 0.3 \\ \hline 1 & 0.25 \\ \hline 2 & 0.25 \\ \hline 3 & 0.2 \\ \hline \end{tabular}

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Problem 231

y Statistis (FALL 2 2024) Kerlise Sylvestre 11/14/24 9:58 PM rmal Distribution Homework Question 16, 6.2.6-T HW Score: $37.84 \%, 14$ of 37 points Points: 0 of 1 Save
Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15 .
The area of the shaded region is $\square$ (Round to four decimal places as needed.) View an example Get more help - Clear all Check answer (1) $74^{\circ} \mathrm{F}$ Clear

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Problem 232

Mykeldine Alcide Kerlise Sylvestre Homework - Google Chrome layerHomeworkaspx?homeworkld=684100659\&questionld=1\&\&lushed =false\&cld=8029729\¢erwin=yes stis (FALL 2 2024) Kerlise Sylvestre 11/14/24 10:05 PM (2) Distribution Homework Question 21, 6.2.11 HW Score: 45.95\%, 17 of 37 points Points: 0 of 1 Save
Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15 .
Click to view page 1 of the table Click to view page 2 of the table.
The indicated IQ score, $x$ , is $\square$ (Round to one decimal place as needed.) ew an example Get more help - Clear all Chock answer

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Problem 233

Kerlise Sylvestre 11/14/24 10:32 PM Question 34, 6.4.13-T HW Score: 84.68\%, 31.33 of 37 points tribution Homework Part 3 of 3 Points: 0.33 of 1 Sav
When women were finally allowed to become pilots of fighter jets, engineers needed to redesign the ejection seats because they had been originally designed for men only. The ejection seats were designed for men weighing between 130 lb and 201 lb . Weights of women are now normally distributed with a mean of 172 lb and a standard deviation of 46 l Complete parts (a) through (c) below. a. If 1 woman is randomly selected, find the probability that her weight is between 130 lb and 201 lb .
The probability is approximately 0.5553 . (Round to four decimal places as needed.) b. If 30 different women are randomly selected, find the probability that their mean weight is between 130 lb and 201 lb.
The probability is approximately 0.9997 . (Round to four decimal places as needed.) c. When redesigning the ejection seat, which probability is more relevant? A. The part (b) probability is more relevant because the seat performance for a single pilot is moresmportant. B. The part (a) probability is more relevant because the seat performance for a sample of pilots is more important. C. The part (a) probability is more relevant because the seat performance for a single pilot is more important D. The part (b) probability is more relevant because the seat performance for a sample of pilots is more important Clear all Chect answer an example Get more help $73^{\circ} \mathrm{F}$ Clear

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Problem 234

Determine whether the random variable $X$ has a binomial distribution. If it does, state the number of trials $n$ . If it does not, explain why not. Twelve students are randomly chosen from an English class of 150 students. Let $X$ be the average number of classes that the students are taking.
Part: $0 / 2$
Part 1 of 2
The random variable (Choose one) 7 a binomial distribution. has does not have

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Problem 235

9. Rafa serves again! Tennis superstar Rafael Nadal's first-serve speeds in a recent season can be modeled by a normal distribution with mean 115 mph and standard deviation 6 mph . Use the empirical rule to approximate the following: (a) The proportion of Rafa's first serves that were faster than 121 mph (b) The percent of Rafa's first serves with speeds between 109 and 133 mph
10. Cholesterol modeled Cholesterol levels for teenage boys can be modeled by a normal distribution with mean $150 \mathrm{mg} / \mathrm{dl}$ and standard deviation

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Problem 236

$\begin{array}{|c|c|c|c|c|} \hline & \text{Male} & \text{Female} & \text{Total} \\ \hline \text{12} & \text{11} & \text{14} & \text{37} \\ \hline \text{4} & \text{18} & \text{16} & \text{38} \\ \hline \text{Total} & \text{16} & \text{29} & \text{30} & \text{75} \\ \hline \end{array}$
If one student was chosen at random, determine the following probabilities. Write your answers as reduced fractions. What is the probability of the student being female?

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Problem 237

\text{Every person has one of eight blood types, determined by molecules on the surface of their red blood cells. Individuals can only receive specific blood types, usually the one that matches their own. Use the circle graph showing the percentage of individuals with each blood type to answer the following.} \\
\text{How much greater is the probability of not selecting an individual with blood type B-negative than not selecting an individual with blood type B-positive?} \\ \text{\$\square\$ (Simplify your answer.)} \\
\text{The user took a picture with their phone and the text was extracted above. The user then had a dialogue with an AI Assistant to help clarify the instructions.} \\
\text{Dialogue Transcript:} \\
\text{It seems that there's a circle graph mentioned in the problem, which should display the percentage of individuals with each blood type. However, since I can't see the graph or know the percentages, I can't calculate the probability differences directly. Could you please provide those specific percentages for B-positive and B-negative blood types? Once you provide those details, I'll be able to help you solve the problem!} \\
\text{Thanks for sharing the information, but I still need the percentages specifically for blood type B-positive and B-negative from the graph. Could you provide these details so I can help you find the probability difference?} \\
\text{Based on the extracted text and the dialogue transcript, please rewrite the math problem that the Assistant is helping the user to solve. Rewrite it in LaTeX. Do not omit any portion of the original problem. When you have finished writing the problem, type the special keyword:}

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Problem 238

The table shows the educational attainment of the population of a certain country, ages 25 and over, expressed in millions. Find the probability that a randomly selected person, aged 25 or over, has completed four years of high school only or is male.
Male Female Total \begin{tabular}{|c|c|c|c|c|} \hline \multicolumn{4}{|c|}{ Years of High School } & \multicolumn{1}{|c|}{ Years of College } \\ \multirow{2}{*}{ Less than 4 } & 4 only & Some (less than 4) & 4 or more & Total \\ \hline 12 & 24 & 21 & 22 & 79 \\ \hline 13 & 31 & 20 & 23 & 87 \\ \hline 25 & 55 & 41 & 45 & 166 \\ \hline \end{tabular}
The probability is $\square$ (Type an integer or a simplified fraction.)

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Problem 239

2) Compute: $p(0.8<z<2.19)$ . You must sketch, shade, and label a bell curve for credit. 3) Find the missing z-number: $p(z<c)=0.7$ . You must sketch, shade, and label a bell curve for credit.

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Problem 240

The duration of a professor's class has continuous uniform distribution between 49.2 minutes and 55.5 minutes. If one class is randomly selected and the probability that the duration of the class is longer than a certain number of minutes is 0.361 , then find the duration of the randomly selected class, i.e., if $P(x>c)=0.361$ , then find $c$ , where $c$ is the duration of the randomly selected class. Round your answer to one decimal places. $c=$ $\square$ minutes

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Problem 241

Given that $X \sim B(45,0.38)$ , find each of the following probabilities. Give results accurate to at least 4 decimal places. $P(X=11)$ $\square$ $P(X \leq 18)$ $\square$ $P(X \geq 16)$ $\square$

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Problem 242

Given that $X \sim B(25,0.65)$ , find each of the following probabilities. Give results accurate to at least 4 decimal places. $P(X=19)$ $\square$ $P(X \leq 14)$ $\square$ $P(X \geq 12)$ $\square$

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Problem 243

Part 2 or 3
Thirteen jurors are randomly selected from a population of 3 million residents. Of these 3 million residents, it is known that $43 \%$ are of a minority race. Of the 13 jurors selected, 2 are minorities. (a) What proportion of the jury described is from a minority race? (b) If 13 jurors are randomly selected from a population where $43 \%$ are minorities, what is the probability that 2 or fewer jurors will be minorities? (c) What might the lawyer of a defendant from this minority race argue? (a) The proportion of the jury described that is from a minority race is 15. $\square$ (Round to two decimal places as needed.) (b) The probability that 2 or fewer out of 13 jurors are minorities, assuming that the proportion of the population that are minorities is $43 \%$ , is $\square$ (Round to four decimal places as needed.)

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Problem 244

Use $n=6$ and $p=0.5$ to complete parts (a) through (d) below. (a) Construct a binomial probability distribution with the given parameters. \begin{tabular}{cc} $\mathbf{x}$ & $\mathbf{P ( x )}$ \\ \hline 0 & $\square$ \\ \hline 1 & $\square$ \\ \hline 2 & $\square$ \\ \hline 3 & $\square$ \\ \hline 4 & $\square$ \\ \hline 5 & $\square$ \\ \hline 6 & $\square$ \\ \hline \end{tabular} (Round to four decimal places as needed.)

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Problem 245

5.2 Check Your Understanding
1. Suppose we choose an American adult at random. Define two events: $A=$ the person has a cholesterol level of 240 milligrams per deciliter of blood ( $\mathrm{mg} / \mathrm{dl}$ ) or above (high cholesterol) $B=$ the person has a cholesterol level of 200 to $<240 \mathrm{mg} / \mathrm{dl}$ (borderline high cholesterol)
According to the American Heart Association, $P(A)=0.16$ and $P(B)=0.29$ a) Explain why events $A$ and $B$ are mutually exclusive. b) Say in plain language what the event " $A$ or $B$ " is. Then find $P(A$ or $B)$ . c) Let $C$ be the event that the person chosen has a cholesterol level below $200 \mathrm{mg} / \mathrm{dl}$ (normal cholesterol). Find $P(C)$ .

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Problem 246

$2 X \sim N\left(\mu, 15^{2}\right)$ . Given that $P(X<90)=0.1$ , determine $\mu$ . $3 X \sim N\left(40, \sigma^{2}\right)$ . Given that $P(X>50)=0.01$ , determine $\mu$ . $4 X \sim N\left(\mu, \sigma^{2}\right)$ . Given that $P(X<5)=0.05$ and $P(X>10)=0.01$ , determine $\mu$ and $\sigma$ .

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Problem 247

SAT math scores follow a normal distribution with a mean of of 500 and a standard deivation of 100 . Suppose we choose a student at random.
What is the probability that the student scores more than 700?

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Problem 248

BASIC PROBABILITY: CARDS, DIE, SPINNERS 1) A card is drawn from a standard deck. Find each probability, simplifying the fractions. \begin{tabular}{|c|c|c|} \hline The card is a red 4. & The card is a diamond. & The card is a king and a \\ heart. \end{tabular} 2) A die is rolled. Find each probability, simplifying the fractions.

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Problem 249

ACT math scores follow a normal distribution with a mean of of 18 and a standard deivation of 6 . Suppose we choose a student at random.
What is the probability that the student scores between 14 and 22?

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Problem 250

GRE scores follow a normal distribution with a mean of of 1000 and a standard deivation of 200. Suppose we choose a student at random.
What is the probability that the student scores between 900 and $1300 ?$

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Problem 251

You pay $\$ 1.00$ to play a game in which you roll one fair die. If you roll a 6 on the first roll, you win $\$ 5.00$ . If you roll a 1 or a 2 , you win $\$ 2.00$ . If not, you lose your money.
3 Multiple Choice 1 point What is the expected value of this game? \$0.25 \$0.50 -\$0.50 -\$1.00

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Problem 252

The transaction history at an electronic goods store indicates that 21 percent of customers purchase the extended warranty when they buy an eligible item. Suppose customers who buy eligible items are chosen at random, one at a time, until one is found who purchased the extended warranty. Let the random variable $X$ represent the number of customers it takes to find one who purchased the extended warranty. Assume customers' decisions on whether to purchase the extended warranty are independent. Which of the following is closest to the probability that $X>3$ ; that is, the probability that it takes more than 3 customers who buy an eligible item to find one who purchased the extended warranty? (A) 0.131 (B) 0.390 (C) 0.493 (D) 0.507 (E) 0.624

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Problem 253

A recent report indicated that 22 percent of the households in a certain community speak a language other than English at home. A reporter will randomly select a household from the community until the first household that speaks a language other than English at home is selected. Let random variable $Q$ represent the number of attempts needed until the first household that speaks a language other than English at home is selected. The random variable $Q$ has a geometric distribution with $p=0.22$ . Which of the following is closest to the variance of the random variable? (A) 0.0484
B 3.5454 (C) 4.0144 (D) 4.5455 (E) 16.1157

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Problem 254

We have a deck of 8 cards numbered from 1 to 8 . Some are white and some are grey, as shown below. 12 34
5 6 7 8
The cards numbered $1,4,6$ , and 8 are white. The cards numbered $2,3,5$ , and 7 are grey. Answer the following questions. Write each answer as a fraction.
A card will be drawn at random. (a) What is the probability that the card drawn is grey? $\square$ (b) What is the probability that the card drawn is grey, given that an evennumbered card is drawn? $\square$

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Problem 255

78. The probability that a marksman will hit a target each time he shoots is 0.89 . If he fires 15 times, what is the probability that he hits the target at most 13 times?

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Problem 256

Jse for \# 8-11 It is commonly accepted that $70 \%$ of all apartment dwellers in Gotham City deadbolt their doors in addition to locking them as an added precaution against burglary. A newpaper story reports that a recent survey of 20 idomly selected apartment dwellers in Kings, one of the boroughs of the city, found that 16 of the 20 respondents deadbolt their doors. The reporter concluded that "since 16 out of 20 is $80 \%$ , it seems that Kings residents are more worried about burglary than the city as a whole." We want to use simulation to test this conclusion by determining how likely it would be to select a sample of 20 with 16 or more deadbolters from a population where only $70 \%$ are deadbolters.
8. Describe in words how you would use the table of random digits below to simulate a single simple random sample of 20 apartment dwellers (one trial).
9. Use the random digit table reproduced below to simulate an SRS of 20 apartment dwellers. You may show your work on the table or make a separate listing. \begin{tabular}{llllll} 71487 & 09984 & 29077 & 14863 & 61683 & 47052 \\ 62224 & 51025 & 35476 & 55972 & 39421 & 65850 \\ 4266 & 35435 & 43742 & 11937 & & \end{tabular}
10. How many people were deadbolters in your simulated sample from \#9?
11. For timed-test purposes, this was only one trial. Carefully describe how you would conduct the entire simulation to answer the question at hand if you had a larger table of random digits and more time.

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Problem 257

Mail works as an IT technician for a local company. There are 1000 computers on the company's network and 958 of them are not infected with a wirus Mai chooses a computer on the company's notwork at random. Tef the event $A$ and the event $B$ he act followe. A: The computer Mal chooses is not infected with the virus. B: The computer Mai chooses is infected with the virus. Find the following probabilities. Write vour answers as deelmal numbers and do not round. $P(A)=$ $\square$ $P(B)=$ $\square$

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Problem 258

Real estate ads suggest that $51 \%$ of homes for sale have garages, $36 \%$ have swimming pools, and $33 \%$ have both features. What percentage of homes for sale have a) a pool or a garage?
Answer = $\square$ \% b) neither a pool nor a garage?
Answer = $\square$ \% c) a pool but no garage?
Answer = $\square$ \%
Note: Enter your answers as percentages, not decimals.

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Problem 259

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 ).
Click here to view the standard normal distribution table (page 1), Click here to view the standard normal distribution table (page 2). (c) What is the probability that a random sample of 22 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.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. A. If 100 different samples of $n=22$ 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. B. If 100 different samples of $n=22$ 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. C. If 100 different samples of $n=22$ 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. (d) What effect does increasing the sample size have on the probability? Provide an explanation for this result. A. Increasing the sample size decreases the probability because $\sigma_{\bar{x}}$ increases as $n$ increases. B. Increasing the sample size increases the probability because $\sigma_{\bar{x}}$ increases as $n$ increases.

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Problem 260

Use this table or the ALEKS calculator to complete the following. Give your answers to four decimal places (for example, 0.1234). (a) Find the area under the standard normal curve to the right of $z=0.85$ . $\square$ (b) Find the area under the standard normal curve between $z=0.82$ and $z=2.20$ .

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Problem 261

LEKS 4.5: Statistics \& Unit 4 R ALEKS Quiz 4 (Statistics) ALEKS - Jorge Mandujano - Lea Wow! www-awu.aleks.com/alekscgi/x/sl.exe/1o_u-lgNslkasNW8D8A9PVfh-8q3gyGHU3RuYLjKQkQoiOk1A8mqLVs492_RhY1of4ZFuDMOAwRJjpunuqw-1ivxImx3RJ_LHHK0VaRofAbM8-9D... Stalisties $3 / 5$ Jorge Finding a probability given a normal distribution: Basic Español
Suppose that resting pulse rates among healthy adults are normally distributed with a mean of 72 beats per minute and a standard deviation of 25 beats per minute. Use this table or the ALEKS calculator to find the percentage of healthy adults who have resting pulse rates that are more than 109 beats per minute. For your intermediate computations, use four or more decimal places. Give your final answer to two decimal places (for example $98.23 \%$ ). $\square$ 【％ \%

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Problem 262

Question 4 of 15 (1 point) I Question Attempt: 1 of 3 Blood types: The blood type 0 negative is called the "universal donor" type, because it is the only blood type that may safely be transfused into any person. Therefore, when someone needs a transfusion in an emergency and their blood type cannot be determined, they are given type O negative blood. For this reason, donors with this blood type are crucial to blood banks. Unfortunately, this blood type is fairly rare; according to the Red Cross, only $5 \%$ of U.S. residents have type $O$ negative blood. Assume that a blood bank has recruited 19 donors. Round the answers to at least four decimal places.
Part 1 of 3 (a) What is the probability that two or more of them have type 0 negative blood?
The probability that two or more of them have type $O$ negative blood is 0.2452
Part 2 of 3 (b) What is the probability that fewer than five of them have type 0 negative blood?
The probability that fewer than five of them have type 0 negative blood is 0.9980 .
Part: $2 / 3$
Part 3 of 3 (c) Would it be unusual if none of the donors had type 0 negative blood? Use a cutoff of 0.05 .

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Problem 263

Use this table or the ALEKS calculator to complete the following. Give your answers to four decimal places (for example, 0.1234). (a) Find the area under the standard normal curve to the right of $z=-0.45$ . $0.3264$ (b) Find the area under the standard normal curve between $z=0.82$ and $z=2.20$ . $-0.1922$

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Problem 264

Pay Your bills: A company audit showed that of 637 bills that were sent out, 373 were paid on time, 109 were paid up to 30 days late, 77 were paid between 31 and 90 days late, and 78 remained unpaid after 90 days. One bill is selected at random.
Part: $0 / 2$ $\square$
Part 1 of 2 (a) What is the probability that the bill was paid on time? Round your answer to four decimal places.
The probability that the bill was paid on time is $\square$ .

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Problem 265

In the game of roulette, a player can place a $\$ 4$ bet on the number 4 and have a $\frac{1}{38}$ probability of winning. If the metal ball lands on 4 , the player gets to keep the $\$ 4$ paid to play the game and the player is awarded an additional $\$ 140$ . Otherwise, the player is awarded nothing and the casino takes the player's $\$ 4$ . What is the expected value of the game to the player? If you played the game 1000 times, how much would you expect to lose?
The expected value is $\$$ $\square$ . (Round to the nearest cent as needed.) The player would expect to lose about $\$$ $\square$ (Round to the nearest cent as needed.)

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Problem 266

Submit test
Assume the random variable $X$ is normally distributed with mean $\mu=50$ and standard deviation $\sigma=7$ . Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded. $P(X>41)$
Which of the following normal curves corresponds to $P(X>41)$ ? A. B. $\frac{45}{41-50}$ C. $P(X>41)=$ $\square$ (Round to four decimal places as needed.)

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Problem 267

1.47. Në një pikë karburanti ka tre tipe gazesh, $40 \%$ e klientēve blejnĕ gaz tê tipit tê parë, $35 \%$ e klientëve blejnë gaz të tipit të dytë, $25 \%$ e klientēve blejnë gaz tē tipit të tretë. Një klient mund ta mbushë serbatorin plot ose jo sipas preferencës. Nga përdoruesit e gazit të tipit të parē, $30 \%$ mbushin serbatorin plot, për gazin e tipit tê dytë $60 \%$ dhe për gazin e tipit të tretë $50 \%$ . Gjeni probabilitetit që klienti i radhës tē mbushë serbatorin plot dhe të kërkojë gaz të tipit të dytë.

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Problem 268

A dartboard has 8 equally sized slices numbered from 1 to 8 . Some are grey and some are white. The slices numbered 5, 6, and 7 are grey The slices numbered $1,2,3,4$ , and 8 are white. A dart is tossed and lands on a slice at random. Let $X$ be the event that the dart lands on a grey slice, and let $P(X)$ be the probatilly of $X_{\text {. }}$
Let not $X$ be the event that the dart lands on a slice that is not grey, and let $P($ not $X)$ be the probability of nat $X$ . (a) For each event in the table, check the outcomef(y) that are contained in the event. Then, in the last column, enter \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|} \hline \multirow{2}{}{Event} & \multicolumn{8}{|c|}{Duticames} & \multirow{2}{}{Probability} \\ \hline & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & \\ \hline X & 5 & & $\square$ & 4 & 5 & 57. & (4) & 4 & $P(x)=\square$ \\ \hline not $X$ & $\square$ & 4 & 4 & D & (1) & (4) & 0 & (4) & $P(\operatorname{not} X)=\square$ \\ \hline \end{tabular} (b) Subtract. $1-P(X)=$ $\square$ (c) Select the answer that makes the sentence true. $1-P(X)$ is the same as (Choose one) $\square$

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Problem 269

(d) $P(|X-Y|=1)$ .
320. Supozoni se tre ndryshore tê rastëstahone $X_{1}, X_{2}$ dhe $X_{3}$ kuné qué shpermalarge tel perbashkèt tẽ vachducshme si vijon: $f\left(x_{1}, x_{2}, x_{3}\right)=\left\{\begin{array}{ll} c\left(x_{1}+2 x_{2}+3 x_{3}\right) & \text { për } 0 \leq x_{i} \leq 1(i=1,2,3) \\ 0 & \text { ndryshe } \end{array}\right.$
Pëncaktoni (a) vlerën e konstantēs c; (b) Funksioni i densitetve për $X_{1}$ dhe $X_{3}$ ; the $P\left(X_{3}<1 / 2 \mid X_{1}=1 / 4, X_{2}=3 / 4\right)$

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Problem 270

A manager records the number of hours, $X$ , each employee works on his or her shift and develops the probability distribution below. Fifty people work for the manager. How many people work 4 hours per shift? \begin{tabular}{|c|c|} \hline \multicolumn{2}{|c|}{ Probability Distribution } \\ \hline \begin{tabular}{c} Hours \\ Worked: $\boldsymbol{X}$ \end{tabular} & Probability: $P(X)$ \\ \hline 3 & 0.1 \\ \hline 4 & $?$ \\ \hline 5 & 0.14 \\ \hline 6 & 0.3 \\ \hline 7 & 0.36 \\ \hline 8 & 0.06 \\ \hline \hline \end{tabular} 0 1 2 4

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Problem 271

The scores of the students on a standardized test are normally distributed, with a mean of 500 and a standard deviation of 110 . What is the probability that a randomly selected student has a score between 350 and 550 ? Use the portion of the standard normal table below to help answer the question. \begin{tabular}{|c|c|} \hline $z$ & Probability \\ \hline 0.00 & 0.5000 \\ \hline 0.25 & 0.5987 \\ \hline 0.35 & 0.6368 \\ \hline 0.45 & 0.6736 \\ \hline 1.00 & 0.8413 \\ \hline 1.26 & 0.8961 \\ \hline 1.35 & 0.9115 \\ \hline 1.36 & 0.9131 \\ \hline \hline \end{tabular} $9 \%$ $24 \%$ $59 \%$

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Problem 272

For a standard normal distribution, which of the following expressions must always be equal to 1? $P(z \leq-a)-P(-a \leq z \leq a)-P(z \geq a)$ $P(z \leq-a)-P(-a \leq z \leq a)+P(z \geq a)$ $P(z \leq-a)+P(-a \leq z \leq a)-P(z \geq a)$ $P(z \leq-a)+P(-a \leq z \leq a)+P(z \geq a)$

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Problem 273

Risk taking is an important part of investing. In order to make suitable investment decisions on behalf of their customers, portfolio managers give a questionnaire to new customers to measure their desire to take financial risks. The scores on the questionnaire are approximately normally distributed with a mean of 51 and a standard deviation of 16 . The customers with scores in the bottom $15 \%$ are described as "risk averse." What is the questionnaire score that separates customers who are considered risk averse from those who are not? Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place. $\square$

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Problem 274

Use the Standard Normal Table or technology to find the z-score that corresponds to the cumulative area 0.8170. $z=$ $\square$ (Type an integer or decimal rounded to two decimal places as needed.)

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Problem 275

Use the Standard Normal Table or technology to find the $z$ -score that corresponds to the following cumulative area. $0.9006$
The cumulative area corresponds to the z-score of $\square$ (Round to three decimal places as needed.)

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Problem 276

Use the standard normal table to find the z-score that corresponds to the given percentile. If the area is not in the table, use the entry closest to the area. If the area is halfway between two entries, use the z-score halfway between the corresponding z-scores. If convenient, use technology to find the z-score. $P_{15}$
Click to view page 1 of the table. Click to view page 2 of the table.
The $z$ -score that corresponds to $\mathrm{P}_{15}$ is $\square$ (Round to two decimal places as needed.)

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Problem 277

Find the indicated z-score shown in the graph to the right.
The z-score is $\square$ (Round to two decimal places as needed.)

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Problem 278

Find the z-score that has $10.2 \%$ of the distribution's area to its left.
The z-score is $\square$ (Round to two decimal places as needed.)

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Problem 279

Find the z-score that has $3.533 \%$ of the distribution's area to its left.
The z-score is $\square$ (Round to two decimal places as needed.)

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Problem 280

The pregnancy durations (in days) for a population of new mothers can be approximated by a normal distribution, with a mean of 272 days and a standard deviation of 9 days. (a) What is the minimum pregnancy durations that can be in the top $8 \%$ of pregnancy durations? (b) What pregnancy durations would be considered unusual?

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Problem 281

Suppose scores on the SAT exam are normally distributed with mean 1100 and standard deviation 200. Answer the following. (a) Aaron scored 1060 on the SAT. What proportion of students performed worse than Aaron? Round to 4 decimal places. (b) Betty scored 1199 on the SAT. What proportion of students performed better than Betty? Round to 4 decimal places. $\square$ (c) What proportion of students got a score between Aaron's and Betty's scores? Round to 4 decimal places. $\square$

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Problem 282

According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 67 inches and a standard deviation of 2.3 inches. Suppose one Martian adult male is randomly chosen. Let $X=$ height of the individual. 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 the person is between 63.2 and 65.3 inches. $\square$ c. The middle $40 \%$ of Martian heights lie between what two numbers?
Low: $\square$ inches
High: $\square$ inches

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Problem 283

Examples Jennelle draws one card from a standard deck of 52 cards.
1. Determine the probability of drawing either a queen or a king.

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Problem 284

3. 21. Supozojmë se $X$ ka densitet $f(x)=e^{-x}, \quad x>0$ (a) Llogaritni funksionin prodhues të momenteve të $X$ dhe gjeni pritjen matematike, mesataren dhe dispersionin. (b) Gjeni pritjen matematike drejtpërsëdrejti nga përkufizimi.

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Problem 285

For a binomial experiment with a $\mathrm{n}=9$ trials, each with a success probability $\mathrm{p}=0.79$ , what is the probability of obtaining less than 5 successes?
Your answer: 0.404 0.147 0.081 0.024 0.107 0.545 0.976 0.541 0.878 0.189

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Problem 286

a. Of the 100 senators in the U.S. Senate, 59 favor a new bill on health care reform. The opposing senators start a filibuster is the bill likely to pass?
No, it is unlikely the bill will pass because those in favor don't have the needed $3 / 5$ majority to end the fillbuster b A criminal conviction in a particular state requires a vote by $2 / 3$ of the jury members On an 16 -member jury, 12 jurors vote to convict Will the defendant be convicted? Yes, the defendant will be convicled because those voting to convict have $\square$ the required $2 / 3$ of the jury c. A proposed amendment to the U S Constitution has passed both the House and the Senate with more than the required $2 / 3$ super majority Each state holds a vote on the amendment, and it receives a majonty vote in all but 15 of the 50 states Is the Constitution amended? No, the Constitution is not amended because the amendment doesn't have the approval of the needed $3 / 4$ majority of the states d A tax increase bill has the support of 73 out of 100 senators and 289 out of 435 members of the House of Representatives. The President promises to veto the bill if it is passed is it likely to become law? Yes, the bill $\square$ likely to become law because it $\square$ the needed $2 / 3$ super majority in $\square$ the Senate

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Problem 287

27. Annie and Alvie have agreed to meet for lunch between noon (0:00 P.M.) and 1:00 P.M. Denote Annie's arrival time by $X$ . Alvie's by $Y$ , and suppose $X$ and $Y$ are independent with pdf's $\begin{array}{l} f_{X}(x)=\left\{\begin{array}{cl} 3 x^{2} & 0 \leq x \leq 1 \\ 0 & \text { otherwise } \end{array}\right. \\ f_{X}(y)=\left\{\begin{array}{rl} 2 y & 0 \leq y \leq 1 \\ 0 & \text { otherwise } \end{array}\right. \end{array}$
What is the expected amount of time that the one who arrives first must wait for the other person? [Hint: $\quad h(X, Y)=|X-Y|$ .

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Problem 288

This exercise is on probabilities and coincidence of shared bithdays. Complete parts (a) through (e) below. a. If two people are selected at random, the probability that they do not have the same birthday (day and month) is $\frac{365}{365} \cdot \frac{364}{365}$ . Explain why this is so. (Ignore leap years and assume 365 days in a year.)
The first person can have any birthday, so they can have a birthday on $\square$ of the 365 days. In order for the second person to not have the same birthday they must have one of the $\square$ remaining birthdays. (Type whole numbers.)

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Problem 289

The numbered disks shown are placed in a box and one disk is selected at random. Find the probability of selecting a 4, given that a green disk is selected.
Find the probability of selecting a 4 , given that a green disk is selected. $\square$ (Type an integer or a simplified fraction.)

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Problem 290

A single die is rolled twice. Find the probability of rolling an even number the first time and a number greater than 5 the second time.
Find the probability of rolling an even number the first time and a number greater than 5 the second time. $\square$ (Type an integer or a simplified fraction.)

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Problem 291

Elizabeth brought a box of donuts to share. There are two-dozen (24) donuts in the box, all identical in size, shape, and color. Five are jelly-filled, 9 are lemon-filled, and 10 are custard-filled. You randomly select one donut, eat it, and select another donut. Find the probability of selecting a jelly-filled donut followed by a custard-filled donut. $\square$ (Type an integer or a simplified fraction.)

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Problem 292

his exercise is on probabilities and coincidence of shared birthdays. Complete parts (a) through (e) bel a. If two people are selected at random, the probability that they do not have the same birthday (day and $n$ $\frac{365}{365} \cdot \frac{364}{365}$ . Explain why this is so. (Ignore leap years and assume 365 days in a year.) The first person can have any birthday, so they can have a birthday on $365^{\circ}$ of the 365 days. In order for the person to not have the same birthday they must have one of the 364 remaining birthdays. (Type whole numbers.) b. If six people are selected at random, find the probability that they all have different birthdays.
The probability that they all have different birthdays is $0.960^{\circ}$ . (Round to three decimal places as needed.) c. If six people are selected at random. find the probability that at least two of them have the same birthday.
The probability that at least two of them have the same birthday is $\square$ (Round to three decimal places as needed.)

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Problem 293

In a large casino, the house wins on its blackjack tables with a probability of $50.8 \%$ . All bets at blackjack are 1 to 1 , which means that if you win, you gain the amount you bet, and if you lose, you lose the amount you bet. a. If you bet $\$ 1$ on each hand, what is the expected value to you of a single game? What is the house edge? b. If you played 450 games of blackjack in an evening, betting $\$ 1$ on each hand, how much should you expect to win or lose? c. If you played 450 games of blackjack in an evening, betting $\$ 10$ on each hand, how much should you expect to win or lose? d. If patrons bet $\$ 7,000,000$ on blackjack in one evening, how much should the casino expect to eam? a. The expected value to you of a single game is $\$-0.016$ . (Type an integer or a decimal) The house edge is $\$ 0.016$ (Type an integer or a decimal.) b. You should expect to lose $\$ \square$ . (Type an integer or a decimal.)

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Problem 294

Fill in the blank so that the resulting statement is true. The theoretical probability of event $E$ , denoted by $\qquad$ is the $\qquad$ divided by $\qquad$ $\qquad$
The theoretical probability of event $E$ , denoted by $\square$ is the $\square$ divided by $\square$

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Problem 295

The table below shows the educational attainment of a country's population, aged 25 and over. Use the data in the table, expressed in millions, to find the probability that a randomly selected citizen, aged 25 or over, was a man with less than 4 years of high school. \begin{tabular}{|l|c|c|c|c|c|} \hline & \begin{tabular}{c} Less Than \\ 4 Years \end{tabular} & \begin{tabular}{c} 4 Years \\ High School \\ Only \end{tabular} & \begin{tabular}{c} Some College \\ (Less Than \\ 4 Years) \end{tabular} & \begin{tabular}{c} 4 Years \\ College \\ (or More) \end{tabular} & \begin{tabular}{c} Total \end{tabular} \\ \hline Male & 14 & 22 & 20 & 25 & 81 \\ \hline Female & 17 & 28 & 23 & 18 & 86 \\ \hline Total & 31 & 50 & 43 & 43 & 167 \\ \hline \end{tabular}
The probability that a randomly selected citizen, aged 25 or over, was a man with less than 4 years of high school is $\square$ (Type an integer or a simplified fraction.)

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Problem 296

Sickle cell anemia is an inherited disease in which red blood cells become distorted and deprived of oxygen. A person with two sickle cell genes will have the disease, but a person with only one sickle cell gene will have a mild, non-fatal anemia called sickle cell trait. Using S to represent a healthy gene, and s the sickle cell gene, the table shows the four possibilities for the children of two Ss parents. Find the probability that these parents give birth to a child who has sickle cell anemia. \begin{tabular}{|cc|cc|} \hline & & \multicolumn{2}{|c|}{ Second } \\ & Parent \\ S & s \\ \hline First & S & SS & Ss \\ Parent & s & sS & ss \\ \hline \end{tabular} $P($ child has sickle cell anemia $)=$ $\square$ (Simplify your answer.)

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Problem 297

Suppose that 1700 people are all playing a game for which the chance of winning is $46 \%$ . Complete parts (a) and (b) below. a. Assuming everyone plays exactly five games, what is the probability of one person winning five games in a row? $\mathrm{P}($ five wins in a row $)=$ $\square$ (Round to three decimal places as needed.)

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Problem 298

Determine whether the statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.
When working problems involving probability with permutations, the denominators of the probability fractions consist of the total number of possible permutations.
Choose the correct answer below. A. The statement is true B. The statement is false. When working problems involving probability with permutations, the numerators of the probability fractions consist of the total number of possible permutations. C. The statement is false. When working problems involving probability with combinations, the numerators of the probability fractions consist of the total number of possible permutations. D. The statement is false. When working problems involving probability with combinations, the denominators of the probability fractions consist of the total number of possible permutations.

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Problem 299

A box contains 15 transistors, 4 of which are defective. If 4 are selected at random, find the probability of the statements below. a. All are defective b. None are defective a. The probability is $\square$ (Type a fraction. Simplify your answer.)

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Problem 300

Consider a Bernoulli scheme of 4000 trials, with the probability of success in a single trial equal to $1 / 4$ . Then
a. The probability that at least 2001 trials will end in success is the same as the probability that at most 1999 trials will end in success.
b. The most probable number of sucesses in this experiment amounts to 1000 c. The probability of not obtaining any successes can be approximated using the Poisson theorem with an appropriate expression for $\lambda=4000 / 4$ , and this will be a good approximation. d. Probability of not getting any successes amounts to (3/4)^4000

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Probability

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Find the zzz-score that has 67.4%67.4 \%67.4% of the distribution's area to its right.The z -score is □\square□ 0.07 (Round to two decimal places as needed.)

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Problem 209

Given that Kieran saw exactly one of these types of animal, what is the probability that he saw a lion? Give your answer as a fraction in its simplest form.Zoam PreviousWatch video

Problem 210

82%82 \%82% 65%65 \%65% 35%35 \%35% 18%18 \%18%

Problem 211

Assume a coin is tossed three times. Compute the probability of tails and 2 heats me OOO 118 318 813 Desf Next Page

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Problem 219

What value of zzz divides the standard normal distribution so that half the area is on one side and half is on the other? Round your answer to two decimal places.

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5. The odds against a new car needing major repairs in the next few years are 24 to 1. What is the probability that the car will need major repairs in the next few years?

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2) Compute: p(0.8<z<2.19)p(0.8<z<2.19)p(0.8<z<2.19). You must sketch, shade, and label a bell curve for credit. 3) Find the missing z-number: p(z<c)=0.7p(z<c)=0.7p(z<c)=0.7. You must sketch, shade, and label a bell curve for credit.

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Problem 241

Given that X∼B(45,0.38)X \sim B(45,0.38)X∼B(45,0.38), find each of the following probabilities. Give results accurate to at least 4 decimal places. P(X=11)P(X=11)P(X=11) □\square□ P(X≤18)P(X \leq 18)P(X≤18) □\square□ P(X≥16)P(X \geq 16)P(X≥16) □\square□

Problem 242

Given that X∼B(25,0.65)X \sim B(25,0.65)X∼B(25,0.65), find each of the following probabilities. Give results accurate to at least 4 decimal places. P(X=19)P(X=19)P(X=19) □\square□ P(X≤14)P(X \leq 14)P(X≤14) □\square□ P(X≥12)P(X \geq 12)P(X≥12) □\square□

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Problem 247

SAT math scores follow a normal distribution with a mean of of 500 and a standard deivation of 100 . Suppose we choose a student at random.What is the probability that the student scores more than 700?

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Problem 249

ACT math scores follow a normal distribution with a mean of of 18 and a standard deivation of 6 . Suppose we choose a student at random.What is the probability that the student scores between 14 and 22?

Problem 250

GRE scores follow a normal distribution with a mean of of 1000 and a standard deivation of 200. Suppose we choose a student at random.What is the probability that the student scores between 900 and 1300?1300 ?1300?

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78. The probability that a marksman will hit a target each time he shoots is 0.89 . If he fires 15 times, what is the probability that he hits the target at most 13 times?

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Find the $z$ -score that has $67.4 \%$ of the distribution's area to its right.
The z -score is $\square$ 0.07 (Round to two decimal places as needed.)

Given that Kieran saw exactly one of these types of animal, what is the probability that he saw a lion? Give your answer as a fraction in its simplest form.
Zoam Previous
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$82 \%$ $65 \%$ $35 \%$ $18 \%$

What value of $z$ divides the standard normal distribution so that half the area is on one side and half is on the other? Round your answer to two decimal places.

2) Compute: $p(0.8<z<2.19)$ . You must sketch, shade, and label a bell curve for credit. 3) Find the missing z-number: $p(z<c)=0.7$ . You must sketch, shade, and label a bell curve for credit.

Given that $X \sim B(45,0.38)$ , find each of the following probabilities. Give results accurate to at least 4 decimal places. $P(X=11)$ $\square$ $P(X \leq 18)$ $\square$ $P(X \geq 16)$ $\square$

Given that $X \sim B(25,0.65)$ , find each of the following probabilities. Give results accurate to at least 4 decimal places. $P(X=19)$ $\square$ $P(X \leq 14)$ $\square$ $P(X \geq 12)$ $\square$

SAT math scores follow a normal distribution with a mean of of 500 and a standard deivation of 100 . Suppose we choose a student at random.
What is the probability that the student scores more than 700?

ACT math scores follow a normal distribution with a mean of of 18 and a standard deivation of 6 . Suppose we choose a student at random.
What is the probability that the student scores between 14 and 22?

GRE scores follow a normal distribution with a mean of of 1000 and a standard deivation of 200. Suppose we choose a student at random.
What is the probability that the student scores between 900 and $1300 ?$

Use the Standard Normal Table or technology to find the z-score that corresponds to the cumulative area 0.8170. $z=$ $\square$ (Type an integer or decimal rounded to two decimal places as needed.)