Question 1

Is the roll of a fair die random? Why or why not?

Accepted Answer

A) Yes.You can predict the outcome beforehand. 
B) No.You can usually predict the outcome on one of six attempts. 
C) Yes.You cannot predict the outcome beforehand. 
D) No.There is always a bias in a person's rolling technique. 
E) No.A 3 or 4 is the most likely outcome. 
A) Yes.You can predict the outcome beforehand. 
B) No.You can usually predict the outcome on one of six attempts. 
C) Yes.You cannot predict the outcome beforehand. 
D) No.There is always a bias in a person's rolling technique. 
E) No.A 3 or 4 is the most likely outcome. C

Question 2

Six men and three women are waiting to be interviewed for jobs.If they are all selected in random order,find the probability that all the women will be interviewed first.Your simulation should use at least 10 runs.

Accepted Answer

A)  $\frac { 1 } { 56 }$ 
B)  $\frac { 1 } { 84 }$ 
C)  $\frac { 1 } { 14 }$ 
D)  $\frac { 1 } { 28 }$ 
E)  $\frac { 2 } { 3 }$ 
A)  $\frac { 1 } { 56 }$ 
B)  $\frac { 1 } { 84 }$ 
C)  $\frac { 1 } { 14 }$ 
D)  $\frac { 1 } { 28 }$ 
E)  $\frac { 2 } { 3 }$ B

Question 3

A person with type O-negative blood can donate blood to anyone who needs it,regardless of blood type.About 7% of the U.S.population has type O-negative blood.Your workplace is hosting a blood drive this afternoon.How many potential donors do you expect they will have to examine in order to get 3 units of type O-negative blood?

Accepted Answer

A) 2187 people 
B) 43 people 
C) 21 people 
D) 343 people 
E) 0.21 people 
A) 2187 people 
B) 43 people 
C) 21 people 
D) 343 people 
E) 0.21 people B

Question 4

For each time up at bat,a baseball player has a 70% chance of making an out,a 10% chance of getting walked,and a 20% chance of getting a hit.Estimate the probability that,out of 5 at-bats,the player gets at least one hit.Use 30 simulation runs.

Accepted Answer

A) About 90% 
B) About 20% 
C) About 30% 
D) 100% 
E) About 70% 
A) About 90% 
B) About 20% 
C) About 30% 
D) 100% 
E) About 70%

Question 5

A surprise quiz was given yesterday in your biology class with 8 multiple choice questions.A classmate who took it claimed to have guessed on every question,but got them all correct.Each question had 5 possible answers.Should you believe him? Explain,basing your argument on a simulation involving at least 10 runs.

Accepted Answer

A) No,the possibility of that happening is very small,about 1.51571657. 
B) Yes,it is likely. 
C) It is hard to tell.The simulation would need to have more than 10 runs. 
D) No,the possibility of that happening is very small,about 0.00000256. 
E) Yes,it is possible. 
A) No,the possibility of that happening is very small,about 1.51571657. 
B) Yes,it is likely. 
C) It is hard to tell.The simulation would need to have more than 10 runs. 
D) No,the possibility of that happening is very small,about 0.00000256. 
E) Yes,it is possible.

Question 6

Criticize the following simulation: A student uses a random number from 5 to 13 to simulate the shoe sizes of a population of females.

Accepted Answer

A) The simulation will not model the real situation.It will predict too many small sizes and too many large sizes.Extremes in foot size are not all that common. 
B) The simulation will not model the real situation.Some females have foot sizes that fall outside of the range. 
C) The simulation will not model the real situation.The shoes size of a particular female is unpredictable and cannot be modeled. 
D) The simulation will not model the real situation.To accurately model the population,the simulation should also account for the foot width. 
E) The simulation should model the real situation. 
A) The simulation will not model the real situation.It will predict too many small sizes and too many large sizes.Extremes in foot size are not all that common. 
B) The simulation will not model the real situation.Some females have foot sizes that fall outside of the range. 
C) The simulation will not model the real situation.The shoes size of a particular female is unpredictable and cannot be modeled. 
D) The simulation will not model the real situation.To accurately model the population,the simulation should also account for the foot width. 
E) The simulation should model the real situation.

Question 7

Criticize the following simulation: A student simulates math test scores by choosing a random number between 0 and 100.

Accepted Answer

A) The simulation should model the real situation. 
B) The simulation probably will not model the real situation.For example,the simulation will predict just as many scores between 10 and 20 as between 70 and 80.In reality,the distribution of grades will not be so uniform. 
C) The simulation probably will not model the real situation.Most students dislike math. 
D) The simulation cannot model the real situation.The test performance of an individual student is inherently unpredictable. 
E) The simulation will not model the real situation.It fails to account for the amount of time each student spent studying for the exam. 
A) The simulation should model the real situation. 
B) The simulation probably will not model the real situation.For example,the simulation will predict just as many scores between 10 and 20 as between 70 and 80.In reality,the distribution of grades will not be so uniform. 
C) The simulation probably will not model the real situation.Most students dislike math. 
D) The simulation cannot model the real situation.The test performance of an individual student is inherently unpredictable. 
E) The simulation will not model the real situation.It fails to account for the amount of time each student spent studying for the exam.

Question 8

When drawing five cards randomly from a deck,which is more likely,a royal flush or a full house? A royal flush is the five highest cards of a single suit.A full house is three of one denomination and two of another.How could you simulate 5-card hands? Once you have picked one card,you cannot pick that same card again.Describe how you will simulate a trial.

Accepted Answer

A) A trial is a single five-card hand.Use five sets of random numbers,ignoring repeated cards. 
B) A trial is a single card.Use random numbers,ignoring repeated cards. 
C) A trial is a single five-card hand.Use one set of random numbers,ignoring repeated cards. 
D) A trial is five-card hands,dealt until the deck is completely dealt.Use five sets of random numbers,ignoring repeated cards. 
E) A trial is a single five-card hand.Use five sets of random numbers. 
A) A trial is a single five-card hand.Use five sets of random numbers,ignoring repeated cards. 
B) A trial is a single card.Use random numbers,ignoring repeated cards. 
C) A trial is a single five-card hand.Use one set of random numbers,ignoring repeated cards. 
D) A trial is five-card hands,dealt until the deck is completely dealt.Use five sets of random numbers,ignoring repeated cards. 
E) A trial is a single five-card hand.Use five sets of random numbers.

Question 9

Criticize the following simulation: A student uses a random number from 1 to 13 to simulate the value of a card drawn at random from a standard deck of playing cards.

Accepted Answer

A) The simulation will not model the real situation.The simulation should use random numbers from 1 to 12. 
B) The simulation will not model the real situation.In reality,there are less "face" cards than cards with numbers. 
C) The simulation might not model the real situation.The deck may not be shuffled,in which case the real situation may not be random. 
D) No criticism.The simulation should model the real situation. 
E) The simulation will not model the real situation.The simulation must also account for the card's suit. 
A) The simulation will not model the real situation.The simulation should use random numbers from 1 to 12. 
B) The simulation will not model the real situation.In reality,there are less "face" cards than cards with numbers. 
C) The simulation might not model the real situation.The deck may not be shuffled,in which case the real situation may not be random. 
D) No criticism.The simulation should model the real situation. 
E) The simulation will not model the real situation.The simulation must also account for the card's suit.

Question 10

What is the probability that Jennifer will have two sons out of her three children? Assume that boy and girl babies are equally likely.Disregard the likelihood that there are more male births and that there is a higher infant mortality rate for boys.Your simulation should use at least 10 runs.

Accepted Answer

A)  $\frac { 1 } { 4 }$ 
B)  $\frac { 3 } { 8 }$ 
C)  $\frac { 1 } { 2 }$ 
D)  $\frac { 5 } { 8 }$ 
E)  $\frac { 1 } { 8 }$ 
A)  $\frac { 1 } { 4 }$ 
B)  $\frac { 3 } { 8 }$ 
C)  $\frac { 1 } { 2 }$ 
D)  $\frac { 5 } { 8 }$ 
E)  $\frac { 1 } { 8 }$

Question 11

Computers generate pseudorandom numbers.Can these numbers be used as random numbers? Why or why not?

Accepted Answer

A) No.Only truly random numbers can be used in statistics. 
B) Yes.They are virtually indistinguishable from truly random numbers. 
C) Yes,so long as the program that generates them does not allow the repetition of numbers in back-to-back sequence. 
D) No,because they are generated in a fixed sequence. 
E) Yes,so long as the program that generates them ensures that all of the prospective numbers are eventually used. 
A) No.Only truly random numbers can be used in statistics. 
B) Yes.They are virtually indistinguishable from truly random numbers. 
C) Yes,so long as the program that generates them does not allow the repetition of numbers in back-to-back sequence. 
D) No,because they are generated in a fixed sequence. 
E) Yes,so long as the program that generates them ensures that all of the prospective numbers are eventually used.

Question 12

A university in your region estimates that graduating average of high school students who apply for admission to a particular university program can be described by a Normal model with a mean of 82% and a standard deviation of 5%.The staff in admissions opens the applications at random looking for 10 applicants with averages above 85%.How many applications do you think the staff will need to open?

Accepted Answer

A) About 36 applications 
B) About 21 applications 
C) About 10 applications 
D) About 28 applications 
E) About 14 applications 
A) About 36 applications 
B) About 21 applications 
C) About 10 applications 
D) About 28 applications 
E) About 14 applications

Question 13

Suppose that there are two candidates for the president of your school's student government,Candidate A and Candidate B.We believe that Candidate A has about a 52% of the votes of the student body.However,you're worried that only 1000 students will show up to vote.How often will Candidate A lose in this situation? To find out,you set up a simulation.Describe the response variable.

Accepted Answer

A) The response variable is the total number of students who vote. 
B) The response variable is the vote of one random voter. 
C) The response variable is the number of votes for Candidate A. 
D) The response variable is whether Candidate A loses or not. 
E) The response variable is the number of votes for Candidate B. 
A) The response variable is the total number of students who vote. 
B) The response variable is the vote of one random voter. 
C) The response variable is the number of votes for Candidate A. 
D) The response variable is whether Candidate A loses or not. 
E) The response variable is the number of votes for Candidate B.

Question 14

When drawing five cards randomly from a deck,which is more likely,a royal flush or a full house? A royal flush is the five highest cards of a single suit.A full house is three of one denomination and two of another.How could you simulate 5-card hands? Once you have picked one card,you cannot pick that same card again.Describe the response variable.

Accepted Answer

A) The response variable is whether the hand had a royal flush or a full house. 
B) The response variable is whether the hand had a full house. 
C) The response variable is whether the hand had neither a royal flush nor a full house. 
D) The response variable is whether the hand had a royal flush. 
E) The response variable is whether the hand had a royal flush,a full house,or neither. 
A) The response variable is whether the hand had a royal flush or a full house. 
B) The response variable is whether the hand had a full house. 
C) The response variable is whether the hand had neither a royal flush nor a full house. 
D) The response variable is whether the hand had a royal flush. 
E) The response variable is whether the hand had a royal flush,a full house,or neither.

Question 15

For a particular miniature golf hole,the chance of getting a hole-in-one is only 18%.The chance of sinking any subsequent putt is 50%.Estimate the average number of putts for this hole.(NOTE: A hole-in-one counts as one putt.)Use 30 runs in your simulation.

Accepted Answer

A) About 3.5 putts 
B) About 4.5 putts 
C) About 4.0 putts 
D) About 2.5 putts 
E) About 1.5 putts 
A) About 3.5 putts 
B) About 4.5 putts 
C) About 4.0 putts 
D) About 2.5 putts 
E) About 1.5 putts

Question 16

You are planning to take the test to be certified to administer CPR.Your teacher has told you that only 35% of candidates pass the test the first time.For those who fail the test on the first try,41% pass on their second attempt.Estimate the percentage of those tested who still are not certified after two attempts.Your simulation should use at least 20 runs.

Accepted Answer

A) 21% 
B) 38% 
C) 76% 
D) 69% 
E) 14% 
A) 21% 
B) 38% 
C) 76% 
D) 69% 
E) 14%

Question 17

You take a surprise quiz in your astronomy class with 12 multiple-choice questions.You estimated that you would have about a 80% chance of getting any individual question correct.What are your chances of getting them all right? Your simulation should use at least 20 runs.

Accepted Answer

A) 9.6 
B) 429,981,696 
C) 96 
D) 7.3003721 
E) 0.06871948 
A) 9.6 
B) 429,981,696 
C) 96 
D) 7.3003721 
E) 0.06871948

Question 18

Suppose that there are two candidates for the president of your school's student government,Candidate A and Candidate B.We believe that Candidate A has about a 52% of the votes of the student body.However,you're worried that only 1000 students will show up to vote.How often will Candidate A lose in this situation? To find out,you set up a simulation.Describe how you will simulate a component and its outcomes.

Accepted Answer

A) The component is one voter voting.An outcome is a vote for Candidate A.Use three random digits,giving 000-599 a vote for Candidate A and 600-999 as no vote 
B) The component is one hundred voters voting.An outcome is a vote for Candidate A.Use one random digit,giving 0-5 as vote for Candidate A and 6-9 as no vote. 
C) The component is one voter voting.An outcome is a vote for the candidate or not.Use three random digits,giving 000-519 as a vote for Candidate A and 520-999 as a vote for Candidate B. 
D) The component is ten voters voting.An outcome is a vote yes or no for the referendum.Use two random digits,giving 00-51 as a vote for Candidate A and 52-99 as a vote for Candidate B. 
E) The component is one voter voting.An outcome is a vote for the candidate or not.Use three random digits,giving 000-520 as a vote for Candidate A and 521-999 as a vote for Candidate B. 
A) The component is one voter voting.An outcome is a vote for Candidate A.Use three random digits,giving 000-599 a vote for Candidate A and 600-999 as no vote 
B) The component is one hundred voters voting.An outcome is a vote for Candidate A.Use one random digit,giving 0-5 as vote for Candidate A and 6-9 as no vote. 
C) The component is one voter voting.An outcome is a vote for the candidate or not.Use three random digits,giving 000-519 as a vote for Candidate A and 520-999 as a vote for Candidate B. 
D) The component is ten voters voting.An outcome is a vote yes or no for the referendum.Use two random digits,giving 00-51 as a vote for Candidate A and 52-99 as a vote for Candidate B. 
E) The component is one voter voting.An outcome is a vote for the candidate or not.Use three random digits,giving 000-520 as a vote for Candidate A and 521-999 as a vote for Candidate B.

Question 19

What is the minimum number of times that an ordinary deck of playing cards must be shuffled to make the deck random?

Accepted Answer

A) 7 
B) 1 
C) 2 
D) 8 
E) It cannot be made random. 
A) 7 
B) 1 
C) 2 
D) 8 
E) It cannot be made random.

Question 20

The lengths of long distance phone calls placed on a cell phone can be described by a Normal model with a mean of 7 minutes and a standard deviation of 2 minutes.If one call is randomly selected from wireless phone company records,what is the probability that it will have lasted more than 11 minutes?

Accepted Answer

A) 0.0977 
B) 0.23 
C) 0.977 
D) 0.023 
E) 0.98 
A) 0.0977 
B) 0.23 
C) 0.977 
D) 0.023 
E) 0.98

Exam 9: Understanding Randomness

Is the roll of a fair die random? Why or why not?

Six men and three women are waiting to be interviewed for jobs.If they are all selected in random order,find the probability that all the women will be interviewed first.Your simulation should use at least 10 runs.

For each time up at bat,a baseball player has a 70% chance of making an out,a 10% chance of getting walked,and a 20% chance of getting a hit.Estimate the probability that,out of 5 at-bats,the player gets at least one hit.Use 30 simulation runs.

Criticize the following simulation: A student uses a random number from 5 to 13 to simulate the shoe sizes of a population of females.

Criticize the following simulation: A student simulates math test scores by choosing a random number between 0 and 100.

Criticize the following simulation: A student uses a random number from 1 to 13 to simulate the value of a card drawn at random from a standard deck of playing cards.

What is the probability that Jennifer will have two sons out of her three children? Assume that boy and girl babies are equally likely.Disregard the likelihood that there are more male births and that there is a higher infant mortality rate for boys.Your simulation should use at least 10 runs.

Computers generate pseudorandom numbers.Can these numbers be used as random numbers? Why or why not?

For a particular miniature golf hole,the chance of getting a hole-in-one is only 18%.The chance of sinking any subsequent putt is 50%.Estimate the average number of putts for this hole.(NOTE: A hole-in-one counts as one putt.)Use 30 runs in your simulation.

You take a surprise quiz in your astronomy class with 12 multiple-choice questions.You estimated that you would have about a 80% chance of getting any individual question correct.What are your chances of getting them all right? Your simulation should use at least 20 runs.

What is the minimum number of times that an ordinary deck of playing cards must be shuffled to make the deck random?

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