Deck 6: Modeling Random Events: the Normal and Binomial Models

Question 1

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.

A)10.7 minutes
B)17.2 minutes
C)13.8 minutes
D)None of these

Answer 1

10.7 minutes

Question 2

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.

A)22.3 minutes
B)18.1 minutes
C)26.0 minutes
D)None of these

Answer 2

22.3 minutes

Question 3

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?

A)Cannot be determined with the given information.
B)Yes, 45 would be an unusually large number of people given the known probability of 0.12.
C)Yes, 45 would be an unusually small number of people given the known probability of 0.115.
D)No, 45 is within the expected range of people.

Answer 3

No, 45 is within the expected range of people.

Question 4

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?

A)Can't be determined with the given information
B)0.50; 0.25
C)0.50; 0.75
D)0.25; 0.50

Question 5

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.

A)0.130
B)0.870
C)0.758
D)None of these

Question 6

The normal model N(58, 21)describes the distribution of weights of chicken eggs in grams. Suppose that the weight of a randomly selected chicken egg has a z- score of - 2.01. What is the weight of this egg in grams? Round to the nearest hundredth of a gram.

A)15.80 grams
B)38.10 grams
C)31.20 grams
D)28.50 grams

Question 7

An MP3 playlist, containing several songs from five genres, is set to shuffle. The following table shows the genre and the associated probability for the first song played. Does the table represent a probability distribution?

A)Yes
B)Can't be determined with the given information
C)No

Question 8

Determine whether the variable would best be modeled as continuous or discrete: The temperature of a cup of coffee dispensed from a beverage vending machine, taken four times during a 24- hour period.

A)Discrete
B)Continuous

Question 9

Determine which of the given procedures describe a binomial distribution.

A)Observing that ten out of the next twenty customers at a grocery store checkout use a credit card given that the probability of using a credit card is 0.58.
B)Record the number of songs downloaded in a month for a group of 30 randomly selected college students.
C)Surveying customers entering a sporting equipment store until a customer responds that he or she was shopping for a bicycle.

Question 10

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.

A)0.552
B)0.048
C)0.287
D)0.213

Question 11

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.

A)7 people, give or take 2 people
B)8 people, give or take 2 people
C)3 people, give or take 4 people
D)7 people, give or take 1 person

Question 12

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?

A)No, this would not be unusual.
B)Yes, this would be unusual.

Question 13

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.

A)0.323
B)0.022
C)0.978
D)0.028

Question 14

Determine whether the variable would best be modeled as continuous or discrete: The number of tomatoes harvested each week from a greenhouse tomato plant.

A)Continuous
B)Discrete

Question 15

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.

A)0.216
B)0.978
C)0.784
D)None of these

Question 16

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)?

A)What percentage of people living and working in Kokomo have a travel time to work that is between thirteen and fifteen minutes?
B)If 15% of people living and working in Kokomo have travel time to work that is below a certain number of minutes, how many minutes would that be?

Question 17

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.

A)63%
B)37%
C)25%
D)None of these.

Question 18

The normal model N(58, 21)describes the distribution of weights of chicken eggs in grams. Suppose that the weight of a randomly selected chicken egg has a z- score of 1.78. What is the weight of this egg in grams? Round to the nearest hundredth of a gram.

A)65.25 grams
B)79.50 grams
C)95.38 grams
D)89.50 grams

Question 19

Which of the following characteristics are not required for the binomial model?

A)The trials must be independent.
B)The probability of success is the same at each trial.
C)The outcome must be a discrete numerical variable.
D)There are a fixed number of trials.

Question 20

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?

A)What percentage of people living and working in Kokomo have a travel time to work that is between thirteen and fifteen minutes?
B)If 15% of people living and working in Kokomo have travel time to work that is below a certain number of minutes, how many minutes would that be?

Question 21

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.

A)0.134
B)0.704
C)0.866
D)0.267

Question 22

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.

A)The probability that a randomly selected can of AJ's whipped cream will weigh between 7.8 ounces and 8.3 ounces is approximately 0.131.
B)Less than 1% of all cans of AJ's whipped cream will weigh more than 8.3 ounces.
C)Approximately 95% of all cans of AJ's whipped cream will weigh between 6.96 ounces and 8.04 ounces.
D)All of these statements are true.

Question 23

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.

A)0.935
B)0.065
C)0.183
D)0.857

Question 24

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.

A)The probability that a randomly selected can of Benneke peaches will weigh between 12.9 ounces and 13.6 ounces is approximately 0.585.
B)About 4% of all cans of Benneke peaches will weigh less than 12.9 ounces
C)Approximately 95% of all Benneke brand canned peaches will weigh between 12.85 ounces and 14.15 ounces.
D)All of these statements are true.

Question 25

Which of the following characteristics are not required for the binomial model?

A)There are a fixed number of trials.
B)The probability of success must be the same as the probability of failure.
C)Only two outcomes are possible at each trial.
D)The trials must be independent.

Question 26

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.

A)15%
B)75%
C)25%
D)None of these.

Question 27

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.

A)10 people, give or take 3 people
B)9 people, give or take 3 people
C)5 people, give or take 2 people
D)10 people, give or take 2 people

Question 28

Determine whether the variable would best be modeled as continuous or discrete: The number of cups dispensed from a beverage vending machine during a 24- hour period.

A)Discrete
B)Continuous

Question 29

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.

A)0.115
B)0.007
C)0.733
D)None of these

Question 30

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.

A)0.480
B)0.998
C)0.035
D)0.264

Question 31

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?

A)No
B)Yes
C)Can't be determined with the given information

Question 32

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.

A)Roughly 15.1% of the basketballs will weigh more than 23.1 ounces.
B)Roughly 36.4% of the basketballs will weigh more than 23.1 ounces.
C)Roughly 13.6% of the basketballs will weigh more than 23.1 ounces.
D)Roughly 42.3% of the basketballs will weigh more than 23.1 ounces.

Question 33

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.

A)5.7% of the basketballs will weigh less than 20.7 ounces.
B)40.3% of the basketballs will weigh less than 20.7 ounces.
C)22.3% of the basketballs will weigh less than 20.7 ounces.
D)9.7% of the basketballs will weigh less than 20.7 ounces.

Question 34

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.

A)0.001
B)0.111
C)0.321
D)None of these

Question 35

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.

A)0.315
B)0.723
C)0.685
D)0.547

Question 36

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?

A)Can't be determined with the given information
B)0.50; 0.25
C)0.50; 0.75
D)0.75; 0.25

Question 37

Determine whether the variable would best be modeled as continuous or discrete: The temperature of a greenhouse at a certain time of the day.

A)Discrete
B)Continuous

Question 38

Determine which of the given procedures describe a binomial distribution.

A)Record the number of ear piercings in a group of 30 randomly selected college students.
B)Surveying customers leaving a hardware store until a customer responds that he or she spent more than fifty dollars.
C)Observing that five out of the next ten customers at a hotdog stand order hot peppers given that the probability of ordering hot peppers is 0.18.

Question 39

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?

A)Yes, this would be unusual.
B)No, this would not be unusual.

Question 40

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?

A)Cannot be determined with the given information.
B)No, 63 is within the expected range of people.
C)Yes, 63 would be an unusually large number of people given the known probability of 0.12.
D)Yes, 63 would be an unusually small number of people given the known probability of 0.12.

Question 41

If a regulation soccer ball is randomly selected, what is the probability that it will have a circumference between 66.9 and 68.9 cm? Round to the nearest thousandth.

Question 42

Explain the difference between a discrete random variable and a continuous random variable and give an example of each.

Question 43

List two requirements that must be satisfied for any probability distribution. Explain how the probability distribution in question (4)satisfies these requirements.

Question 44

Roughly what percentage of regulation soccer balls has a circumference that is greater than
69.9 cm? Round to the nearest tenth of a percent.

Question 45

Suppose the probability that a person does not recycle is 0.23. If 300 randomly selected people were asked "Do you recycle?" would you be surprised if 65 said no to this question? Why?

Question 46

Using the information from question (2), find the probability that the reaction time will occur after fourteen minutes, but before fifteen minutes. Shade the appropriate area and calculate the numerical value of the probability.

Question 47

Would it be unusual to randomly select a regulation soccer ball and find that it has a circumference that is greater than 72.3 cm?

Question 48

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.

Question 49

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?

Question 50

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?

Question 51

The normal model N(210,45)describes the weights of baby elephants in pounds. Suppose that the weight of a randomly selected baby elephant has a z- score of - 1.35. What is the weight of this baby elephant in pounds? Round to the nearest tenth of a pound.

Question 52

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.

Question 53

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.

Question 54

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.

Question 55

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.

Question 56

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.

Question 57

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.

Question 58

List the four characteristics of the binomial model.

Question 59

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.

Question 60

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.