## Introductory Statistics

Statistics

## Quiz 6 :

Modeling Random Events

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Q01 Q01 Q01

Use the following information for the question. The average travel time to work for a person living and working in Kokomo, Indiana is 17 minutes. Suppose the standard deviation of travel time to work is 4.5 minutes and the distribution of travel time is approximately normally distributed.
-Which of these statements is asking for a probability?

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A

Q02 Q02 Q02

Use the following information to answer the question. Suppose that the probability that a person books an airline ticket using an online travel website is 0.72. For the questions that follow, consider a sample of ten randomly selected people who recently booked an airline ticket.
-Out of ten randomly selected people, how many would you expect to use an online travel website to book their hotel, give or take how many? Round to the nearest whole person.

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D

Q03 Q03 Q03

Use the following information for the question. The average travel time to work for a person living and working in Kokomo, Indiana is 17 minutes. Suppose the standard deviation of travel time to work is 4.5 minutes and the distribution of travel time is approximately normally distributed.
-Which of these statements is asking for a measurement (i. e. is an inverse normal question)?

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B

Q04 Q04 Q04

Use the following information to answer the question. Suppose that the probability that a person books a hotel using an online travel website is 0.68. For the questions that follow, consider a sample of fifteen randomly selected people who recently booked a hotel.
-What is the probability that at least fourteen out of fifteen people used an online travel website when they booked their hotel? Round to the nearest thousandth.

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Q07 Q07 Q07

Use the following information for the question. Male players at the high school, college and professional ranks use a regulation basketball that weighs 22.0 ounces with a standard deviation of 1.0 ounce. Assume that the weights of basketballs are approximately normally distributed.
-Would it be unusual to randomly select a regulation basketball and find that it weighs 23.75 ounces?

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Q08 Q08 Q08

Five identical poker chips are tossed in a hat and mixed up. Two of the chips have been marked with an X to indicate that if drawn a valuable prize will be awarded. If you and two of your friends each draws a chip (with replacement), what is the probability that at least one of your group of three will win the valuable prize? Round to the nearest thousandth.

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Q09 Q09 Q09

Use the following information for the question. The average travel time to work for a person living and working in Kokomo, Indiana is 17 minutes. Suppose the standard deviation of travel time to work is 4.5 minutes and the distribution of travel time is approximately normally distributed.
-Suppose that it is reported in the news that 8% of the people living and working in Kokomo feel "very satisfied" with their commute time to work. What is the travel time to work that separates the bottom 8% of people with the shortest travel times and the upper 92%? Round to the nearest tenth of a minute.

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Q10 Q10 Q10

Use the following information to answer the question. Suppose that the probability that a person books a hotel using an online travel website is 0.68. For the questions that follow, consider a sample of fifteen randomly selected people who recently booked a hotel.
-What is the probability that exactly ten people out of fifteen people used an online travel website when they booked their hotel? Round to the nearest thousandth.

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Q12 Q12 Q12

Use the following information for the question. The average travel time to work for a person living and working in Kokomo, Indiana is 17 minutes. Suppose the standard deviation of travel time to work is 4.5 minutes and the distribution of travel time is approximately normally distributed.
-Approximately what percentage of people living and working in Kokomo have a travel time to work that is less than 15.5 minutes? Round to the nearest whole percent.

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Q15 Q15 Q15

Use the following information for the question. The average travel time to work for a person living and working in Kokomo, Indiana is 17 minutes. Suppose the standard deviation of travel time to work is 4.5 minutes and the distribution of travel time is approximately normally distributed.
-Suppose that it is reported in the news that 12% of the people living and working in Kokomo feel that their commute is too long. What is the travel time to work that separates the top 12% of people with the longest travel times and the lower 88%? Round to the nearest tenth of a minute.

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Q16 Q16 Q16

Use the following information for the question. The average travel time to work for a person living and working in Kokomo, Indiana is 17 minutes. Suppose the standard deviation of travel time to work is 4.5 minutes and the distribution of travel time is approximately normally distributed.
-Suppose that the probability that a person between the ages of 19 and 24 buys at least one tabloid magazine per week is 0.115. If 500 randomly selected people between the ages of 19 and 24 were asked "Do you buy at least one tabloid magazine per week?", would you be surprised if 45 or more said yes to this question? Why?

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Q18 Q18 Q18

At a course in public speaking, the instructor always gives an opening speech that lasts between fifteen and eighteen minutes. The length of the speech can be modeled by a uniform distribution, that is, the speech is just as likely to last fifteen minutes as it is to last eighteen minutes. The probability density curve is shown below. What is the probability that the speech will last at least seventeen minutes? What is the probability that the speech will last between fifteen and sixteen minutes?

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Q19 Q19 Q19

Five identical poker chips are tossed in a hat and mixed up. Two of the chips have been marked with an X to indicate that if drawn a valuable prize will be awarded. If you and three of your friends each draws a chip (with replacement), what is the probability that at least one of your group of four will win the valuable prize? Round to the nearest thousandth.

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Q21 Q21 Q21

Use the following information to answer the question. Suppose that the probability that a person books an airline ticket using an online travel website is 0.72. For the questions that follow, consider a sample of ten randomly selected people who recently booked an airline ticket.
-What is the probability that no more than three out of ten people used an online travel website when they book their airline ticket? Round to the nearest thousandth.

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Q23 Q23 Q23

A box containing recipes from five categories is dropped so that the recipe cards are thoroughly mixed up. The following table shows the possible categories and the associated probability for a recipe randomly chosen. Does the table represent a probability distribution?

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Q25 Q25 Q25

At a course in public speaking, the instructor always gives an opening speech that lasts between fifteen and eighteen minutes. The length of the speech can be modeled by a uniform distribution, that is, the speech is just as likely to last fifteen minutes as it is to last eighteen minutes. The probability density curve is shown below. What is the probability that the speech will last sixteen minutes or more? What is the probability that the speech will last between eighteen and nineteen minutes?

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Q26 Q26 Q26

Use the following information to answer the question. Suppose that the probability that a person books a hotel using an online travel website is 0.68. For the questions that follow, consider a sample of fifteen randomly selected people who recently booked a hotel.
-Out of fifteen randomly selected people, how many would you expect to use an online travel website to book their hotel, give or take how many? Round to the nearest whole person.

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Q27 Q27 Q27

Use the following information for the question. Male players at the high school, college and professional ranks use a regulation basketball that weighs 22.0 ounces with a standard deviation of 1.0 ounce. Assume that the weights of basketballs are approximately normally distributed.
-Would it be unusual to randomly select a regulation basketball and find that it weighs 17.9 ounces?

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Q28 Q28 Q28

Use the following information to answer the question. Suppose that the probability that a person books a hotel using an online travel website is 0.68. For the questions that follow, consider a sample of fifteen randomly selected people who recently booked a hotel.
-What is the probability that no more than four out of fifteen people used an online travel website when they booked their hotel? Round to the nearest thousandth.

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Q29 Q29 Q29

Suppose that the probability that a person between the ages of 19 and 24 checks their daily horoscope is 0.12. If 400 randomly selected people between the ages of 19 and 24 were asked "Do you check your daily horoscope?", would you be surprised if 63 or more said yes to this question? Why?

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Q30 Q30 Q30

Use the following information for the question. Male players at the high school, college and professional ranks use a regulation basketball that weighs 22.0 ounces with a standard deviation of 1.0 ounce. Assume that the weights of basketballs are approximately normally distributed.
-Roughly what percentage of regulation basketballs weigh more than 23.1 ounces? Round to the nearest tenth of a percent.

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Q33 Q33 Q33

Suppose that weights of cans of Benneke brand peaches have a population mean of 13.5 ounces and a population standard deviation of 0.33 ounces and are approximately normally distributed. Which of the following statements are correct? Choose the best statement.

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Q34 Q34 Q34

Use the following information to answer the question. Suppose that the probability that a person books an airline ticket using an online travel website is 0.72. For the questions that follow, consider a sample of ten randomly selected people who recently booked an airline ticket.
-What is the probability that at least nine out of ten people used an online travel website when they booked their airline ticket? Round to the nearest thousandth.

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Q35 Q35 Q35

Use the following information for the question. Male players at the high school, college and professional ranks use a regulation basketball that weighs 22.0 ounces with a standard deviation of 1.0 ounce. Assume that the weights of basketballs are approximately normally distributed.
-Roughly what percentage of regulation basketballs weigh less than 20.7 ounces? Round to the nearest tenth of a percent.

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Q36 Q36 Q36

Use the following information to answer the question. Suppose that the probability that a person books an airline ticket using an online travel website is 0.72. For the questions that follow, consider a sample of ten randomly selected people who recently booked an airline ticket.
-What is the probability that exactly seven out of ten people used an online travel website when they booked their airline ticket? Round to the nearest thousandth.

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Q37 Q37 Q37

Suppose that weights of cans of AJ's brand whipped cream have a population mean of 7.5 ounces and a population standard deviation of 0.27 ounces and are approximately normally distributed. Which of the following statements are correct? Choose the best statement.

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Q38 Q38 Q38

Use the following information for the question. Male players at the high school, college and professional ranks use a regulation basketball that weighs 22.0 ounces with a standard deviation of 1.0 ounce. Assume that the weights of basketballs are approximately normally distributed.
-If a regulation basketball is randomly selected, what is the probability that it will weigh between 19.5 and 22.5 ounces? Round to the nearest thousandth.

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Q39 Q39 Q39

Use the following information for the question. The average travel time to work for a person living and working in Kokomo, Indiana is 17 minutes. Suppose the standard deviation of travel time to work is 4.5 minutes and the distribution of travel time is approximately normally distributed.
-Approximately what percentage of people living and working in Kokomo have a travel time to work that is at least 20 minutes? Round to the nearest whole percent.

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Q40 Q40 Q40

Use the following information for the question. Male players at the high school, college and professional ranks use a regulation basketball that weighs 22.0 ounces with a standard deviation of 1.0 ounce. Assume that the weights of basketballs are approximately normally distributed.
-If a regulation basketball is randomly selected, what is the probability that it will weigh between 20.5 and 23.5 ounces? Round to the nearest thousandth.

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Q41 Q41 Q41

Use the following information to answer the question. Suppose that weights of jars of Puff brand marshmallow cream has a population mean of 24.5 ounces and a population standard deviation of 0.19 ounces and are approximately normally distributed. Use the figure below to find determine the specified probabilities.
-What is the probability that a randomly selected jar of Puff marshmallow cream will be greater than 24.45 ounces? What is the probability that a randomly selected jar of Puff marshmallow cream will be less than 24.22 ounces? Round to the nearest thousandth.

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Q43 Q43 Q43

Use the following information for the question. Suppose that the probability that the train travelling from Holland, Michigan to Chicago, Illinois arrives on time is 0.80. For the questions that follow, consider a sample of twenty randomly selected train trips.
-What is the probability that exactly fifteen trips out of twenty will arrive in Chicago on time? Round to the nearest thousandth.

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Q46 Q46 Q46

Use the following information for the question. Suppose that the probability that the train travelling from Holland, Michigan to Chicago, Illinois arrives on time is 0.80. For the questions that follow, consider a sample of twenty randomly selected train trips.
-What is the probability that at least nineteen trips out of twenty arrive to Chicago on time? Round to the nearest thousandth.

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Q48 Q48 Q48

Use the following information for the question. Suppose that the probability that the train travelling from Holland, Michigan to Chicago, Illinois arrives on time is 0.80. For the questions that follow, consider a sample of twenty randomly selected train trips.
-Approximately how many trips would you expect to arrive on time out of twenty randomly selected trips, give or take how many trips? Round to the nearest whole trip.

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Q51 Q51 Q51

Use the following information for the question. On a busy day, the average roller coaster wait time at a large amusement park is 27 minutes. Suppose the standard deviation of wait time is 11.9 minutes and the distribution of wait times is approximately normally distributed.
-If it is a busy day, approximately what percentage of people at the amusement park will have a wait time that is at least 30 minutes? Round to the nearest whole percent.

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Q52 Q52 Q52

Use the following information to answer the question. Suppose that weights of jars of Puff brand marshmallow cream has a population mean of 24.5 ounces and a population standard deviation of 0.19 ounces and are approximately normally distributed. Use the figure below to find determine the specified probabilities.
-If a large random sample of Puff marshmallow cream jars were weighed, approximately what percentage of the jars would weigh between 24.22 and 24.45 ounces? Round to the nearest tenth of a percent.

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Q53 Q53 Q53

A suit of standard playing cards has thirteen cards. Suppose the suit of hearts is thoroughly shuffled and that you have the opportunity to play the following game: You win $10 if you choose the ten or queen of hearts, you lose $5 if you choose the jack or king of hearts, you win $2 if you choose the five or seven of hearts, and you lose $10 if you choose the ace of hearts. With any other outcome you will win or lose nothing. Complete the table that shows the probability distribution. Would it be sensible to play this game?

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Q54 Q54 Q54

Use the following information for the question. On a busy day, the average roller coaster wait time at a large amusement park is 27 minutes. Suppose the standard deviation of wait time is 11.9 minutes and the distribution of wait times is approximately normally distributed.
-To improve customer satisfaction, the amusement park manager has decided to give food coupons to customers with long wait times. The manager decides to give the coupons to the top 10% of people waiting the longest. What is the minimum wait time for the top 10%? Round to the nearest tenth of a minute.

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Q55 Q55 Q55

When exposed to heat, the reaction time of a certain chemical always occurs after thirteen minutes, but before 17 minutes. Reaction times for this chemical can be modeled by a uniform distribution, that is, the reaction time is just as likely to occur at thirteen minutes as it is to occur at seventeen minutes. Find the probability that the reaction will happen after fifteen minutes. Shade the appropriate area and calculate the numerical value of the probability.

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Q58 Q58 Q58

At a county animal shelter, the probability that a stray cat comes into the shelter with rabies is 0.145 and the probability that a stray dog comes into the shelter with rabies is
0.157. A volunteer at the shelter records whether the next thirty cats or dogs delivered to the shelter has rabies. Which of the condition or conditions for use of the binomial model is or are not met?

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Q59 Q59 Q59

Use the following information for the question. Suppose that the probability that the train travelling from Holland, Michigan to Chicago, Illinois arrives on time is 0.80. For the questions that follow, consider a sample of twenty randomly selected train trips.
-What is the probability that thirteen or less trips out of twenty arrive on time to Chicago? Round to the nearest thousandth.

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