Deck 16: Probability Models

Question 1

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.

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.

Answer 1

Yes

Question 2

Suppose that in a certain population 8% of people are color blind.A researcher selects people at random from this population.What's the probability that the first color blind person will be found among the first 6 people checked?

A)0.3936
B)0.0527
C)0.6064
D)0.6591
E)0.0485

Answer 2

0.3936

Question 3

A basketball player has made 65% of his foul shots during the season.Assuming the shots are independent,find the probability that in tonight's game he makes his first basket on one of his first 4 shots.

A)0.09612
B)0.02787
C)0.17851
D)0.98499
E)0.01501

Answer 3

0.98499

Question 4

We draw a card from a deck 40 times to find the distribution of the suits.After each draw the card is replaced.

A)Yes.
B)No.More than two outcomes are possible.
C)No.The draws are not independent of each other.
D)No.40 is more than 10% of 52
E)No.The chance of getting each suit changes from one draw to the next.

Question 5

Suppose that in a certain population 45% of people have type O blood.A researcher selects people at random from this population.What is the probability that there is a person with type O blood among the first 6 people checked?

A)0.0277
B)0.0226
C)0.0083
D)0.0503
E)0.9723

Question 6

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?

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

Question 7

A tennis player makes a successful first serve 90% of the time.Assume that each serve is independent of the others.If she serves 10 times,what is the probability that she misses for the first time on her second or fourth serve?

A)0.1
B)0.0066
C)0.1629
D)0.6
E)0.0101

Question 8

Suppose that in a certain population 46% of people have type O blood.A researcher selects people at random from this population.What's the probability they won't find a person with type O blood among the first 4 people checked?

A)0.0724
B)0.9552
C)0.0850
D)0.0448
E)0.9150

Question 9

An archer is able to hit the bull's-eye 71% of the time.If she shoots 10 arrows,what is the probability that her first bull's-eye comes on the 5th arrow? Assume each shot is independent of the others.

A)0.00146
B)0.00502
C)0.07369
D)0.00707
E)0.71

Question 10

You roll a die 7 times and need to get at least three 2's to win the game.

A)Yes
B)No.3 is more than 10% of 7
C)No.The chance of a getting a 2 changes with each roll of the die.
D)No.More than two outcomes are possible on each roll of the die.
E)No.The rolls are not independent of each other.

Question 11

Suppose a computer chip manufacturer rejects 3% of the chips produced because they fail presale testing.What is the probability that the seventh chip you test is the first bad one you find?

A)0.0250
B)0.03
C)0.21
D)0.0007
E)0.0219

Question 12

A pool of possible jurors consists of 15 men and 18 women.A jury of 12 is picked at random from this group.What is the probability that the jury contains all women?

A)Yes
B)No.15 is more than 10% of 18
C)Yes,assuming the possible jurors are unrelated
D)No.There are more than two possible outcomes.
E)No.The chance of a woman changes depending on who has already been picked.

Question 13

We record the blood types (O,A,B,or AB)found in a group of 100 people.Assume that the people are unrelated to each other.

A)Yes.
B)No.The chance of getting a particular blood group changes from one person to the next.
C)No.More than two outcomes are possible.
D)No,400 is more than 10% of the population.
E)No.The chance of getting a particular blood group depends on the blood groups already recorded.

Question 14

We draw a card from a deck 6 times (replacing the card after each draw)and get 3 kings.How likely is this?

A)Yes.
B)No.More than two outcomes are possible.
C)No.The chance of getting a king changes as cards are drawn.
D)No.6 is more than 10% of 52
E)No.The draws are not independent of each other.

Question 15

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.

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 16

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

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 17

A basketball player has made 78% of his foul shots during the season.Assuming the shots are independent,find the probability that in tonight's game he misses for the first time on his 5th attempt?

A)0.22
B)0.0814
C)0.2887
D)0.0635
E)0.3702

Question 18

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?

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

Question 19

How likely is it that in a group of 400 people,the majority have blue eyes,given that 22% of the population have blue eyes? Assume that the people are unrelated to each other.

A)Yes.
B)No.200 is more than 10% of the population.
C)No.More than two outcomes are possible.
D)No.The chance of blue eyes changes from one person to the next.
E)No.More than 10% of the population have blue eyes.

Question 20

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.

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 21

A beginning archer is able to hit the bull's-eye 41% of the time.If she shoots 7 arrows,what is the probability that she gets at most 3 bull's-eyes? Assume each shot is independent of the others.

A)0.6906
B)0.0625
C)0.3094
D)0.2923
E)0.3983

Question 22

An archer is able to hit the bull's eye 65% of the time.If she keeps shooting arrows until she hits the bull's-eye,how long do you expect it will take? Assume each shot is independent of the others.

A)2.86 shots
B)0.35 shots
C)1.54 shots
D)0.65 shots
E)65 shots

Question 23

A test consists of 10 true/false questions.If a student guesses on each question,what is the probability that the student will answer at least 6 questions correctly.

A)0.172
B)0.205
C)0.828
D)0.377
E)0.6

Question 24

A multiple choice test has 6 questions each of which has 4 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 none of the questions correctly?

A)0.1780
B)0.2621
C)0.0445
D)0.9997559
E)0.0002441

Question 25

At one college,66% of students have credit cards.A credit card company,looking for new customers,sets up a booth at the college.If they pick students at random,how many students should they expect to talk to before finding one who does not have a credit card?

A)66
B)2.94
C)34
D)0.34
E)1.52

Question 26

A tennis player makes a successful first serve 57% of the time.If she serves 6 times,what is the probability that she gets all her first serves in? Assume that each serve is independent of the others.

A)0.0063
B)0.9657
C)0.2058
D)0.0147
E)0.0343

Question 27

Suppose that 10% of people are left handed.If 5 people are selected at random,what is the probability that exactly 2 of them are left handed?

A)0.1458
B)0.0729
C)0.0100
D)0.0073
E)0.0081

Question 28

A basketball player has made 75% of his foul shots during the season.Assuming the shots are independent,find the expected number of shots until he misses.

A)0.75
B)25
C)1.33
D)4
E)0.25

Question 29

A multiple choice test has 9 questions each of which has 4 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 exactly 3 questions correctly?

A)0.7664
B)0.0156
C)0.2336
D)0.0028
E)0.3003

Question 30

An archer is able to hit the bull's-eye 48% of the time.If she shoots 8 arrows,what is the probability that she gets exactly 4 bull's-eyes? Assume each shot is independent of the others.

A)0.0531
B)0.2717
C)0.0039
D)0.2355
E)0.7283

Question 31

Suppose that 74% of tax returns are free of errors.How many returns should an IRS auditor expect to check before finding one with errors?

A)3.85
B)74
C)26
D)0.74
E)1.35

Question 32

Suppose that in one city,79% of cars parked at meters still have time remaining on the meter.How many cars should a meter maid expect to check before finding one at an expired meter?

A)0.79
B)79
C)21
D)4.76
E)1.27

Question 33

A company finds that 74% of applicants for a job do not have the required qualifications.How many applications should they expect to read before finding a suitably qualified applicant?

A)0.26
B)74
C)3.85
D)0.74
E)1.35

Question 34

A tennis player makes a successful first serve 54% of the time.If she serves 5 times,what is the probability that she gets exactly 3 first serves in? Assume that each serve is independent of the others.

A)0.0333
B)0.3332
C)0.1575
D)0.2838
E)0.6668

Question 35

Suppose a computer chip manufacturer rejects 4% of the chips produced because they fail presale testing.How many chips should they expect to test before finding a bad one?

A)1.04
B)4
C)25
D)0.04
E)0.96

Question 36

In one city,the probability that a person will pass his or her driving test on the first attempt is 0.68.11 people are selected at random from among those taking their driving test for the first time.What is the probability that among these 11 people,the number passing the test is between 2 and 4 inclusive?

A)0.0057
B)0.0345
C)0.0299
D)0.0251
E)0.0308

Question 37

A tennis player makes a successful first serve 64% of the time.If she serves 6 times,what is the probability that she gets no more than 3 first serves in? Assume that each serve is independent of the others.

A)0.2446
B)0.6268
C)0.1286
D)0.8714
E)0.3732

Question 38

Suppose that 14% of students at one college have high blood pressure.If you keep picking students at random from this college,how many students do you expect to test before finding one with high blood pressure?

A)14
B)0.14
C)1.16
D)0.86
E)7.14

Question 39

Find the probability of at least 2 girls in 10 births.Assume that male and female births are equally likely and that the births are independent events.

A)0.989
B)0.011
C)0.044
D)0.1
E)0.945

Question 40

A laboratory worker finds that 1.4% of his blood samples tested positive for the HIV virus.How many blood samples should he expect to test before finding one which tests positive for the HIV virus?

A)1.01
B)71.43
C)0.986
D)1.4
E)98.6

Question 41

Suppose a computer chip manufacturer rejects 3% of the chips produced because they fail presale testing.If you test 3 chips,what is the probability that none of the chips fail?

A)0.97
B)0.03
C)2.7 ×

D)0.09
E)0.9127

Question 42

Suppose a computer chip manufacturer rejects 15% of the chips produced because they fail presale testing.If you test 3 chips,what is the probability that not all of the chips fail?

A)0.45
B)0.9966
C)0.6141
D)3.375 ×

E)0.15

Question 43

A car insurance company has determined that 7% of all drivers were involved in a car accident last year.If 11 drivers are randomly selected,what is the probability that at least 3 were involved in a car accident last year?

A)0.0317
B)0.4871
C)0.0695
D)0.9683
E)0.9630

Question 44

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 all of her first serves?

A)0.175
B)0.0053
C)0.1160
D)0.65
E)0.325

Question 45

In a study,38% of adults questioned reported that their health was excellent.A researcher wishes to study the health of people living close to a nuclear power plant.Among 10 adults randomly selected from this area,only 3 reported that their health was excellent.Find the probability that when 10 adults are randomly selected,3 or fewer are in excellent health.

A)0.4336
B)0.3093
C)0.2017
D)0.5664
E)0.2319

Question 46

A company manufactures batteries in batches of 10 and there is a 3% rate of defects.Find the mean number of defects per batch.

A)0.29
B)9.7
C)0.31
D)3.0
E)0.3

Question 47

A company purchases shipments of machine components and uses this acceptance sampling plan: Randomly select and test 20 components and accept the whole batch if there are fewer than 3 defectives.If a particular shipment of thousands of components actually has a 4% rate of defects,what is the probability that this whole shipment will be accepted?

A)0.9561
B)0.0439
C)0.0364
D)0.5141
E)0.1458

Question 48

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?

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

Question 49

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 doesn't make all of the shots?

A)0.3
B)0.0007
C)0.18
D)0.1176
E)0.8824

Question 50

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?

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

Question 51

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.

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

Question 52

Suppose a computer chip manufacturer rejects 3% of the chips produced because they fail presale testing.If you test 4 chips,what is the probability that all of the chips fail?

A)0.03
B)0.08853
C)0.97
D)8.1 ×

E)0.12

Question 53

Police estimate that 25% of drivers drive without their seat belts.If they stop 4 drivers at random,find the probability that all of them are wearing their seat belts.

A)0.1
B)0.3164
C)0.3
D)0.75
E)0.0039

Question 54

A tennis player makes a successful first serve 65% of the time.Assume that each serve is independent of the others.If she serves 3 times,what is the probability that she does not make all of her first serves?

A)0.0429
B)0.7254
C)0.105
D)0.2746
E)0.65

Question 55

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?

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

Question 56

Suppose a computer chip manufacturer rejects 5% of the chips produced because they fail presale testing.If we select 50 chips at random,how many chips do you expect to fail the testing?

A)0.05 chips
B)21.8 chips
C)2.5 chips
D)5 chips
E)2 chips

Question 57

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?

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

Question 58

Police estimate that 65% of drivers wear their seat belts.If they stop 4 drivers at random,what's the probability that none of them are wearing their seat belts?

A)0.1785
B)0.26
C)0.0150
D)0.4
E)0.35

Question 59

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.

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

Question 60

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?

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

Question 61

Police estimate that in one city 48% of drivers wear their seat belts.They set up a safety roadblock,stopping cars to check for seat belt use.If they stop 70 cars during the first hour,what is the mean of the number of drivers expected to be wearing their seat belts?

A)4.18
B)17.47
C)33.6
D)36.4
E)35

Question 62

Suppose the probability of a major earthquake on a given day is 1 out of 10,000.What's the expected number of earthquakes in the next 2,000 days?

A)

B)5
C)20
D)

E)

Question 63

An archer is able to hit the bull's eye 77% of the time.If she shoots 6 arrows,what is the standard deviation of the number of bull's-eyes that she gets? Assume the shots are independent of each other.

A)1.38
B)3
C)4.62
D)1.03
E)1.0626

Question 64

The probability that a radish seed will germinate is 0.7.A gardener plants seeds in batches of 4.Find the standard deviation of the number of seeds germinating in each batch.

A)0.794
B)0.784
C)0.210
D)0.906
E)0.917

Question 65

A laboratory worker finds that 1.6% of his blood samples test positive for the HIV virus.In a random sample of 140 blood tests,what is the mean number that test positive for the HIV virus?

A)2.24
B)137.76
C)1.48
D)2.20
E)22.4

Question 66

An archer is able to hit the bull's eye 74% of the time.If she shoots 130 arrows in a competition,is it appropriate to use a normal model to approximate the distribution of the number of bull's-eyes? Assume that shots are independent of each other.

A)Yes;normal model with μ = 33.8 and σ = 25.01 can be used to approximate the distribution
B)No;normal model cannot be used to approximate the distribution because nq < 10
C)Yes;normal model with μ = 96.2 and σ = 5.00 can be used to approximate the distribution
D)No;normal model cannot be used to approximate the distribution because np < 10
E)Yes;normal model with μ = 96.2 and σ = 25.01 can be used to approximate the distribution

Question 67

A tennis player makes a successful first serve 59% of the time.If she serves 29 times,what is the standard deviation of the number of good first serves? Assume that each serve is independent of the others.

A)11.89
B)14.5
C)7.0151
D)17.11
E)2.65

Question 68

A laboratory worker finds that 1.6% of his blood samples test positive for the HIV virus.In a random sample of 130 blood tests,what is the standard deviation of the number that test positive for the HIV virus?

A)2.04672
B)11.31
C)2.08
D)1.44
E)1.43

Question 69

A laboratory worker finds that 1.8% of his blood samples test positive for the HIV virus.If 270 blood samples are selected at random,is it appropriate to use a normal model to approximate the distribution of the number that test positive for the HIV virus?

A)Yes;normal model with μ = 4.86 and σ = 4.77 can be used to approximate the distribution
B)No;normal model cannot be used to approximate the distribution because nq < 10
C)Yes;normal model with μ = 4.86 and σ = 2.18 can be used to approximate the distribution
D)No;normal model cannot be used to approximate the distribution because np < 10
E)Yes;normal model with μ = 265.14 and σ = 2.18 can be used to approximate the distribution

Question 70

Suppose that 2.4% of people are left handed.If 30 people are selected at random,what is the standard deviation of the number of right-handers in the group?

A)0.70272
B)0.72
C)0.85
D)0.84
E)5.41

Question 71

Police estimate that in one city 83% of drivers wear their seat belts.They set up a safety roadblock,stopping cars to check for seat belt use.If they stop 30 cars during the first hour,what is the standard deviation of the number of drivers expected to be wearing their seat belts?

A)5.1
B)24.9
C)4.23
D)2.06
E)4.99

Question 72

A tennis player makes a successful first serve 70% of the time.If she serves 80 times,is it appropriate to use a normal model to approximate the distribution of the number of good first serves? Assume that each serve is independent of the others.

A)No;normal model cannot be used to approximate the distribution because nq < 10
B)Yes;normal model with μ = 56 and σ = 16.80 can be used to approximate the distribution
C)Yes;normal model with μ = 56 and σ = 4.10 can be used to approximate the distribution
D)Yes;normal model with μ = 24 and σ = 16.80 can be used to approximate the distribution
E)No;normal model cannot be used to approximate the distribution because np < 10

Question 73

A tennis player makes a successful first serve 60% of the time.If she serves 25 times,what is the mean of the number of good first serves? Assume that each serve is independent of the others.

A)15
B)10
C)6.00
D)12.5
E)2.45

Question 74

In the town of Blue Valley,7% of female college students suffer from manic-depressive illness.If 170 of the female students are selected at random,what is the mean of the number who suffer from manic-depressive illness?

A)11.07
B)158.1
C)85
D)3.33
E)11.9

Question 75

On a multiple choice test with 15 questions,each question has four possible answers,one of which is correct.For students who guess at all answers,find the standard deviation of the number of correct answers.

A)1.62
B)1.643
C)1.587
D)1.875
E)1.677

Question 76

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?

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 77

Suppose that 11% of people are left handed.If 26 people are selected at random,what is the mean of the number of right-handers in the group?

A)13
B)1.60
C)2.55
D)23.14
E)2.86

Question 78

Suppose the probability of contracting a certain disease is p = 0.0004 for a new case in a given year.What's the expected number of new cases in a year in a town where 4,000 people do not currently have the disease?

A)0.16
B)1.6
C)16
D)0.0004
E)0.10

Question 79

A company manufactures batteries in batches of 23 and there is a 3% rate of defects.Find the standard deviation of the number of defects per batch.

A)0.800
B)0.291
C)0.815
D)0.831
E)0.818

Question 80

In a certain town,8% of female college students suffer from manic-depressive illness.If 230 of the female students are selected at random,what is the standard deviation of the number who suffer from manic-depressive illness?

A)4.11
B)4.29
C)211.6
D)18.4
E)16.93