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 timeis 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 isbetween thirteen and fifteen minutes?
B)If 15% of people living and working in Kokomo have travel time to work that is below acertain number of minutes, how many minutes would that be?

Answer 1

What percentage of people living and working in Kokomo have a travel time to work that isbetween thirteen and fifteen minutes?

Question 2

Suppose that the probability that a person between the ages of 19 and 24 buys at least one tabloidmagazine per week is 0.115. If 500 randomly selected people between the ages of 19 and 24 wereasked "Do you buy at least one tabloid magazine per week?", would you be surprised if 45 or moresaid 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 2

No, 45 is within the expected range of people.

Question 3

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

A) Discrete
B) Continuous

Answer 3

Continuous

Question 4

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 websitewhen they booked their hotel? Round to the nearest thousandth.

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

Question 5

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 6

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 7

The normal modelN(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 theweight 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 8

Use the following information to answer the question. Suppose that the probability that a person books an airline ticket usingan online travel website is 0.72. For the questions that follow, consider a sample of ten randomly selected people whorecently booked an airline ticket.

-Out of ten randomly selected people, how many would you expect to use an online travel websiteto 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 9

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 timeis 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 thebottom 8% of people with the shortest travel times and the upper 92%? Round to the nearest tenthof a minute.

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

Question 10

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 timeis 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 isbetween thirteen and fifteen minutes?
B)If 15% of people living and working in Kokomo have travel time to work that is below acertain number of minutes, how many minutes would that be?

Question 11

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 towork that is less than 15.5 minutes? Round to the nearest whole percent.

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

Question 12

Five identical poker chips are tossed in a hat and mixed up. Two of the chips have been markedwith an X to indicate that if drawn a valuable prize will be awarded. If you and three of yourfriends each draws a chip (with replacement), what is the probability that at least one of your groupof 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 13

At a course in public speaking, the instructor always gives an opening speech that lasts betweenfifteen 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. Theprobability density curve is shown below. What is the probability that the speech will last at leastseventeen minutes? What is the probability that the speech will last between fifteen and sixteenminutes?

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 14

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 15

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 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.

-Suppose that it is reported in the news that 12% of the people living and working in Kokomo feelthat their commute is too long. What is the travel time to work that separates the top 12% of peoplewith 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

Question 17

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 18

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 19

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 20

The normal modelN(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 theweight 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 21

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 timeis 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 22

Suppose that weights of cans of Benneke brand peaches have a population mean of 13.5 ounces anda population standard deviation of 0.33 ounces and are approximately normally distributed. Whichof 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 23

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 24

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 25

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 26

At a course in public speaking, the instructor always gives an opening speech that lasts betweenfifteen 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. Theprobability density curve is shown below. What is the probability that the speech will last sixteenminutes or more? What is the probability that the speech will last between eighteen and nineteenminutes?

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 27

Suppose that the probability that a person between the ages of 19 and 24 checks their dailyhoroscope is 0.12. If 400 randomly selected people between the ages of 19 and 24 were asked "Doyou 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 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 for the question. Male players at the high school, college and professional ranks use aregulation basketball that weighs 22.0 ounces with a standard deviation of 1.0 ounce. Assume that the weights of basketballsare 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 30

Which of the following characteristics are notrequired 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 31

Use the following information for the question. Male players at the high school, college and professional ranks use aregulation basketball that weighs 22.0 ounces with a standard deviation of 1.0 ounce. Assume that the weights of basketballsare 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 32

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 websitewhen they book their airline ticket? Round to the nearest thousandth.

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

Question 33

Use the following information to answer the question. Suppose that the probability that a person books a hotel using anonline travel website is 0.68. For the questions that follow, consider a sample of fifteen randomly selected people whorecently booked a hotel.

-Out of fifteen randomly selected people, how many would you expect to use an online travelwebsite 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 34

Use the following information for the question. Male players at the high school, college and professional ranks use aregulation basketball that weighs 22.0 ounces with a standard deviation of 1.0 ounce. Assume that the weights of basketballsare 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 35

Suppose that weights of cans of AJ's brand whipped cream have a population mean of 7.5 ouncesand 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 36

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 thenearest 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 37

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? $$\begin{array} { | l | l | } \hline \text { Category } & \text { Probability } \\\hline \text { Main Dish } & 0.421 \\\hline \text { Appetizer } & 0.210 \\\hline \text { Desert } & 0.103 \\\hline \text { Salad } & 0.173 \\\hline \text { Vegetable } & 0.093 \\\hline\end{array}$$

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

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 aregulation basketball that weighs 22.0 ounces with a standard deviation of 1.0 ounce. Assume that the weights of basketballsare 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 40

Use the following information to answer the question. Suppose that the probability that a person books an airline ticket usingan online travel website is 0.72. For the questions that follow, consider a sample of ten randomly selected people whorecently 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 41

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

Question 42

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

Question 43

Use the information that follows to answer the question. Circumferences of regulation soccer balls have a mean of 69 cm withas standard deviation of 1.50 cm. Assume that the circumferences of soccer balls are approximately normally distributed.

-Roughly what percentage of regulation soccer balls has a circumference that is greater than69.9 cm?
Round to the nearest tenth of a percent.

Question 44

Use the following information for the question. Suppose that the probability that the train travelling from Holland, Michiganto Chicago, Illinois arrives on time is 0.80. For the questions that follow, consider a sample of twenty randomly selected traintrips.

-What is the probability that thirteen or less trips out of twenty arrive on time to Chicago?
Round to the nearest thousandth.

Question 45

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 twentyrandomly selected trips, give or take how many trips?
Round to the nearest whole trip.

Question 46

Use the following information for the question. On a busy day, the average roller coaster wait time at a large amusementpark is 27 minutes. Suppose the standard deviation of wait time is 11.9 minutes and the distribution of wait times isapproximately normally distributed.

-If it is a busy day, approximately what percentage of people at the amusement park willhave a wait time that is at least 30 minutes?
Round to the nearest whole percent.

Question 47

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, approximatelywhat percentage of the jars would weigh between 24.22 and 24.45 ounces?
Round to the nearest tenth of a percent.

Question 48

List the four characteristics of the binomial model.

Question 49

Use the information that follows to answer the question. Circumferences of regulation soccer balls have a mean of 69 cm withas standard deviation of 1.50 cm. Assume that the circumferences of soccer balls are approximately normally distributed.

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

Question 50

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

Question 51

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

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 at least nineteen trips out of twenty arrive to Chicago on time?
Round to the nearest thousandth.

Question 53

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

Question 54

Use the following information to answer the question. Suppose that weights of jars of Puff brand marshmallow cream has apopulation mean of 24.5 ounces and a population standard deviation of 0.19 ounces and are approximately normallydistributed. Use the figure below to find determine the specified probabilities.

-What is the probability that a randomly selected jar of Puff marshmallow cream will begreater than 24.45 ounces?
What is the probability that a randomly selected jar of Puffmarshmallow cream will be less than 24.22 ounces?
Round to the nearest thousandth.

Question 55

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 ontime?
Round to the nearest thousandth.

Question 56

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

Question 57

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 foodcoupons to customers with long wait times. The manager decides to give the coupons tothe 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 58

At a county animal shelter, the probability that a stray cat comes into the shelter withrabies is 0.145 and the probability that a stray dog comes into the shelter with rabies is0.157. A volunteer at the shelter records whether the next thirty cats or dogs delivered tothe shelter has rabies. Which of the condition or conditions for use of the binomial model isor are not met?

Question 59

A suit of standard playing cards has thirteen cards. Suppose the suit of hearts is thoroughlyshuffled and that you have the opportunity to play the following game:
You win $10 if youchoose the ten or queen of hearts, you lose $5 if you choose the jack or king of hearts, youwin $2 if you choose the five or seven of hearts, and you lose $10 if you choose the ace ofhearts. With any other outcome you will win or lose nothing. Complete the table thatshows the probability distribution. Would it be sensible to play this game?
$$\begin{array} { | l | l | } \hline \text { Winnings } & \text { Probability } \\ \hline + \$ 10 & \\ \hline - \$ 5 & \\ \hline + \$ 2 & \\ \hline - \$ 10 & \\ \hline 0 & \\ \hline \end{array}$$

Question 60

Use the information that follows to answer the question. Circumferences of regulation soccer balls have a mean of 69 cm with as standard deviation of 1.50 cm. Assume that the circumferences of soccer balls are approximately normally distributed.

-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?