Question 1

An archer is able to hit the bull's eye 48% of the time.If she shoots 8 arrows,how many bull's-eyes do you expect her to get? Assume the shots are independent of each other.

Accepted Answer

A) 1.9968 
B) 1.4 
C) 4 
D) 3.84 
E) 4.16

Question 2

An archer is usually able to hit the bull's-eye 82% of the time.He buys a new bow hoping that it will improve his success rate.During the first month of practice with his new bow he hits the bull's-eye 363 times out of 430 shots.Is this evidence that with the new bow his success rate has improved? In other words,is this an unusual result for him? Explain.

Accepted Answer

A) No;we would normally expect him to make 352.6 bull's-eyes with a standard deviation of 63.47.363 is 0.2 standard deviations above the expected value.That's not an unusual result. 
B) Yes;we would normally expect him to make 352.6 bull's-eyes with a standard deviation of 7.97.363 is 1.3 standard deviations above the expected value.That's an unusual result. 
C) Yes;we would normally expect him to make 352.6 bull's-eyes with a standard deviation of 63.47.363 is 0.2 standard deviations above the expected value.That's an unusual result. 
D) No;we would normally expect him to make 352.6 bull's-eyes with a standard deviation of 7.97.363 is 1.3 standard deviations above the expected value.That's not an unusual result. 
E) No;we would normally expect him to make 352.6 bull's-eyes with a standard deviation of 18.78.363 is 0.6 standard deviations above the expected value.That's not an unusual result.

Question 3

The rate of defects among CD players of a certain brand is 1.3%.Use the Poisson approximation to the binomial distribution to find the probability that among 100 such CD players received by a store,there are exactly three defectives.

Accepted Answer

A) 0.1497 
B) 0.0748 
C) 0.0998 
D) 0.9002 
E) 0.1996

Question 4

We wish to predict the outcome of a local mayoral election,and poll 500 of the 4000 likely voters to see how many favor the incumbent.

Accepted Answer

A) Yes,assuming the 500 people are unrelated 
B) No.The probability of success is the same on every trial. 
C) No.The responses are independent 
D) No.There are more than two possible outcomes. 
E) No.500 is more than 10% of 4000.

Question 5

A multiple choice test has 11 questions each of which has 5 possible answers,only one of which is correct.If Judy,who forgot to study for the test,guesses on all questions,what is the probability that she will answer no more than 3 questions correctly?

Accepted Answer

A) 0.839 
B) 0.111 
C) 0.949 
D) 0.617 
E) 0.162

Question 6

An airline estimates that 97% of people booked on their flights actually show up.If the airline books 71 people on a flight for which the maximum number is 69,what is the probability that the number of people who show up will exceed the capacity of the plane?

Accepted Answer

A) 0.6324 
B) 0.3676 
C) 0.6410 
D) 0.1150 
E) 0.2526

Question 7

On one tropical island,hurricanes occur with a mean of 2.37 per year.Assuming that the number of hurricanes can be modeled by a Poisson distribution,find the probability that during the next 2 years the number of hurricanes will be 3.

Accepted Answer

A) 0.2074 
B) 0.0935 
C) 0.1838 
D) 0.1551 
E) 0.0194

Question 8

We deal 6 cards from a deck and get 3 hearts.How likely is this?

Accepted Answer

A) Yes. 
B) No.More than two outcomes are possible. 
C) No.The suit of each card is independent of the suits already obtained. 
D) No.The chance of getting a heart changes as cards are dealt. 
E) No.3 is more than 10% of 6

Question 9

A basketball player has made 70% of his foul shots during the season.If he shoots 4 foul shots in tonight's game,what is the probability that he makes all of the shots?

Accepted Answer

A) 0.0081 
B) 0.12 
C) 0.28 
D) 0.2401 
E) 0.7

Question 10

A tennis player makes a successful first serve 63% of the time.If she serves 8 times,what is the probability that she gets at least 3 first serves in? Assume that each serve is independent of the others.

Accepted Answer

A) 0.8693 
B) 0.0336 
C) 0.1307 
D) 0.0971 
E) 0.9664

Question 11

Suppose a computer chip manufacturer rejects 4% of the chips produced because they fail presale testing.If 135 chips are picked at random,is it appropriate to use a normal model to approximate the distribution of the number of bad chips?

Accepted Answer

A) No;normal model cannot be used to approximate the distribution because np < 10 
B) Yes;normal model with μ = 129.6 and σ = 2.28 can be used to approximate the distribution 
C) Yes;normal model with μ = 5.4 and σ = 2.28 can be used to approximate the distribution 
D) No;normal model cannot be used to approximate the distribution because nq < 10 
E) Yes;normal model with μ = 5.4 and σ = 5.18 can be used to approximate the distribution

Question 12

Suppose that 14% of people are left handed.If 8 people are picked at random,what's the probability that the first lefty is the 8th person chosen?

Accepted Answer

A) 0.1400 
B) 0.0419 
C) 0.2992 
D) 0.0487 
E) 0.3479

Question 13

A basketball player has made 70% of his foul shots during the season.If he shoots 6 foul shots in tonight's game,what is the probability that he makes none of the shots?

Accepted Answer

A) 0.1176 
B) 0.18 
C) 0.42 
D) 0.0007 
E) 0.3

Question 14

A study found that 56% of people working for large companies are dissatisfied with their job.Your manager conducts a survey at your company and finds that 225 of the 440 employees are dissatisfied with their job.

Accepted Answer

A) Yes 
B) No.Employees within the same company are not independent of one another. 
C) No.There are more than two possible outcomes. 
D) No.The chance of getting a dissatisfied employee changes depending on who has already been selected. 
E) No.225 is more than 10% of 440

Question 15

A company realizes that 5% of its pens are defective.In a package of 30 pens,is it likely that more than 6 are defective? Assume that pens in a package are independent of each other.

Accepted Answer

A) Yes 
B) No.6 is more than 10% of 30 
C) No.The pens in a package are dependent on each other. 
D) No,the chance of getting a defective pen changes depending on the pens that have already been selected. 
E) No.There are more than two possible outcomes.

Question 16

In one town,the number of burglaries in a week has a Poisson distribution with a mean of 2.1.Find the probability that in a randomly selected week the number of burglaries is at least three.

Accepted Answer

A) 0.1614 
B) 0.1890 
C) 0.6496 
D) 0.8110 
E) 0.3504

Question 17

A tennis player makes a successful first serve 65% of the time.Assume that each serve is independent of the others.If she serves 5 times,what is the probability that she makes none of her first serves?

Accepted Answer

A) 0.1160 
B) 0.0053 
C) 0.325 
D) 0.35 
E) 0.175

Question 18

Suppose the probability of a major earthquake on a given day is 1 out of 10,000.Use the Poisson model to approximate the probability that there will be at least one major earthquake in the next 2,000 days.

Accepted Answer

A) 0.1813 
B) 0.1637 
C) 0.8187 
D) 0.8363 
E) 0.0175

Question 19

Suppose a computer chip manufacturer rejects 4% of the chips produced because they fail presale testing.What's the probability you find a bad chip within the first 6 you examine?

Accepted Answer

A) 0.0326 
B) 0.8154 
C) 0.2172 
D) 0.0313 
E) 0.7828

Question 20

The probability that a car will have a flat tire while driving through a certain tunnel is 0.00008.Use the Poisson approximation to the binomial distribution to find the probability that among 16,000 cars passing through this tunnel,at least one will have a flat tire.

Accepted Answer

A) 0.7220 
B) 0.6441 
C) 0.2780 
D) 1.6462 
E) 0.3559

Exam 16: Probability Models