Deck 6: The Normal Distribution

Question 1

Compute the standard deviation of the random variable with the given discrete probability

A)13
B)58.5
C)11.25
D)7.6

Answer 1

D

Question 2

The following table presents the probability distribution of the number of vacations Xtaken last year for a randomly chosen family. )

A)0.05
B)0.91
C)0.19
D)0.09

Answer 2

D

Question 3

An investor is considering a $20,000 investment in a start-up company. She estimatesthat she has probability 0.1 of a $15,000 loss, probability 0.05 of a $20,000 profit,probability 0.25 of a $35,000 profit, and probability 0.6 of breaking even (a profit of $0).What is the expected value of the profit?

A)$11,250
B)$13,333
C)$8250
D)$20,250

Answer 3

C

Question 4

Determine whether the table represents a discrete probability distribution. )

A)No
B)Yes

Question 5

Determine whether the table represents a discrete probability distribution. )

A)Yes
B)No

Question 6

Determine the indicated probability for a binomial experiment with the given number oftrials n and the given success probability )

Question 7

An investor is considering a $15,000 investment in a start-up company. She estimatesthat she has probability 0.15 of a $5000 loss, probability 0.15 of a $10,000 loss,probability 0.15 of a $30,000 profit, and probability 0.55 of breaking even (a profit of$0). What is the expected value of the profit?

A)$10,500
B)$6750
C)$5000
D)$2250

Question 8

A survey asked 863 people how many times per week they dine out at a restaurant. The Consider the 863 people to be a population. Let X be the number of times per week a
Person dines out for a person sampled at random from this population. Find the
Probability that a person dines out 4 or more times per week.

A)0.536
B)0.130
C)0.87
D)0.060

Question 9

Compute the mean of the random variable with the given discrete probability distribution. )

A)16.25
B)11.2
C)126.0
D)18

Question 10

Determine whether the random variable described is discrete or continuous.The length in seconds of a randomly-selected TV commercial

A)continuous
B)discrete

Question 11

Determine the indicated probability for a binomial experiment with the given number oftrials n and the given success probability p. )

Question 12

The following table presents the probability distribution of the number of vacations Xtaken last year for a randomly chosen family. )

A)0.29
B)0.56
C)0.71
D)0.85

Question 13

Determine whether the random variable described is discrete or continuous.The number of minutes you must wait in line at the grocery store

A)continuous
B)discrete

Question 14

A survey asked 849 people how many times per week they dine out at a restaurant. The Consider the 849 people to be a population. Let X be the number of times per week a
Person dines out for a person sampled at random from this population. Compute the

A)2.0
B)2.1
C)2.2
D)1.5

Question 15

A survey asked 915 people how many times per week they dine out at a restaurant. The Consider the 915 people to be a population. Let X be the number of times per week a
Person dines out for a person sampled at random from this population. Compute the
Standard deviation

A)2.1
B)1.5
C)1.9
D)2.2

Question 16

A survey asked 876 people how many times per week they dine out at a restaurant. The Consider the 876 people to be a population. Let X be the number of times per week a
Person dines out for a person sampled at random from this population. Find the
Probability that a person does not dine out at all.

A)0.140
B)0.307
C)0
D)0.447

Question 17

Determine whether the random variable described is discrete or continuous.The number of 3-point shots made in a basketball game

A)continuous
B)discrete

Question 18

Fill in the missing value so that the following table represents a probability distribution.

A)0.16
B)0.07
C)0.25
D)0.02

Question 19

Determine whether the table represents a discrete probability distribution. )

A)Yes
B)No

Question 20

Determine whether the random variable described is discrete or continuous.The total value of a set of coins

A)discrete
B)continuous

Question 21

A student takes a true-false test that has 12 questions and guesses randomly at eachanswer. Let X be the number of questions answered correctly. Find P(10 or more)

A)0.0032
B)0.0730
C)0.0193
D)0.9270

Question 22

The Australian sheep dog is a breed renowned for its intelligence and work ethic. It isestimated that 45% of adult Australian sheep dogs weigh 65 pounds or more. A sampleof 15 adult dogs is studied. What is the probability that more than 12 of them weigh 65lb or more?

A)0.9937
B)0.0011
C)0.0063
D)0.0001

Question 23

It is estimated that 25% of households own a riding lawn mower. A sample of 17households is studied. What is the probability that exactly 9 of these own a riding lawnmower?

A)0.9721
B)0.9907
C)0.0279
D)0.0093

Question 24

Determine the indicated probability for a Poisson random variable with the given values of and t .

A) 0.8647
B) 0.1353
C) 0.5940
D) 0.3233

Question 25

Determine the indicated probability for a Poisson random variable with the given values of and t .

A) 0.2807
B) 0.7193
C) 0.7834
D) 0.9212

Question 26

It is estimated that 45% of households own a riding lawn mower. A sample of 10households is studied. What is the standard deviation of the number of households whoown a riding lawn mower?

A)1.5732
B)4.5
C)2.475
D)10

Question 27

Determine the indicated probability for a binomial experiment with the given number oftrials n and the given success probability p. )

Question 28

It is estimated that 45% of households own a riding lawn mower. A sample of 17households is studied. What is the probability that no more than 3 of these own a ridinglawn mower?

A)0.0184
B)0.9816
C)0.9959
D)0.0041

Question 29

A student takes a true-false test that has 15 questions and guesses randomly at eachanswer. Let X be the number of questions answered correctly. Find P(Fewer than 4)

A)0.9408
B)0.0176
C)0.0592
D)0.0037

Question 30

Determine the indicated probability for a Poisson random variable with the given values of and t .

A) 0.3504
B) 0.6496
C) 0.8386
D) 0.7162

Question 31

Determine the indicated probability for a Poisson random variable with the given values of and t .

A) 0.1468
B) 0.1487
C) 0.0005
D) 0.9995

Question 32

Determine the indicated probability for a Poisson random variable with the given values of and t .

A) 0.0255
B) 0.9281
C) 0.0712
D) 0.0719

Question 33

It is estimated that 30% of households own a riding lawn mower. A sample of 17households is studied. What is the mean number of households who own a ridingmower?

A)17
B)5.1
C)3.57
D)1.8894

Question 34

The Australian sheep dog is a breed renowned for its intelligence and work ethic. It isestimated that 45% of adult Australian sheep dogs weigh 65 pounds or more. A sampleof 14 adult dogs is studied. What is the standard deviation of the number of dogs whoweigh 65 lb or more?

A)6.3
B)3.465
C)1.8615
D)14

Question 35

The Australian sheep dog is a breed renowned for its intelligence and work ethic. It isestimated that 40% of adult Australian sheep dogs weigh 65 pounds or more. A sampleof 13 adult dogs is studied. What is the probability that exactly 9 of them weigh 65 lb ormore?

A)0.1845
B)0.9757
C)0.8155
D)0.0243

Question 36

The Australian sheep dog is a breed renowned for its intelligence and work ethic. It isestimated that 45% of adult Australian sheep dogs weigh 65 pounds or more. A sampleof 13 adult dogs is studied. What is the probability that no more than 3 of them weigh 65lb or more?

A)0.9731
B)0.9071
C)0.0929
D)0.0269

Question 37

Determine the indicated probability for a binomial experiment with the given number oftrials n and the given success probability p. )

Question 38

A student takes a true-false test that has 12 questions and guesses randomly at eachanswer. Let X be the number of questions answered correctly.

A)0.1934
B)0.1208
C)0.0002
D)0.2256

Question 39

It is estimated that 45% of households own a riding lawn mower. A sample of 11households is studied. What is the probability that more than 8 of these own a ridinglawn mower?

A)0.939
B)0.0022
C)0.0610
D)0.0148

Question 40

The Australian sheep dog is a breed renowned for its intelligence and work ethic. It isestimated that 30% of adult Australian sheep dogs weigh 65 pounds or more. A sampleof 14 adult dogs is studied. What is the mean number of dogs who weigh 65 lb or more?

A)4.2
B)14
C)1.7146
D)2.94

Question 41

An environmental scientist obtains a sample of water from an irrigation canal thatcontains a certain type of bacteria at a concentration of 8 per milliliter. Find the standarddeviation of the number of bacteria in a 4-milliliter sample.

A)5.7
B)2.8
C)8
D)32

Question 42

The number of typographical errors in a document follows a Poisson distribution with amean of 2 errors per page. Let X represent the number of errors on 3 pages. FindP(Less than 3).

A)0.0174
B)0.0620
C)0.0595
D)0.6767

Question 43

The number of typographical errors in a document follows a Poisson distribution with a mean of 2 errors per page. Let X represent the number of errors on 4 pages. Find P(3) .

A) 0.0573
B) 0.1804
C) 0.8196
D) 0.0286

Question 44

An environmental scientist obtains a sample of water from an irrigation canal thatcontains a certain type of bacteria at a concentration of 5 per milliliter. Find the meannumber of bacteria in a 4-milliliter sample.

A)2.2
B)4.5
C)20
D)5

Question 45

Last year, a manufacturer produced 1,050,000 DVD players. Of these, approximately 4%were defective. Assume that a simple random sample of n = 210 players is drawn. Usethe Poisson approximation to the binomial distribution to compute the mean number ofDVD players that were defective.

A)4
B)0.4
C)8.4
D)2.9

Question 46

Last year, a manufacturer produced 1,900,000 DVD players. Of these, approximately 3%were defective. Assume that a simple random sample of n = 250 players is drawn. Usethe Poisson approximation to the binomial distribution to compute the standard deviationof the number of DVD players that were defective.

A)3
B)7.5
C)2.7
D)1

Question 47

The number of typographical errors in a document follows a Poisson distribution with amean of 2 errors per page. Let X represent the number of errors on 3 pages. FindP(Greater than 1).

A)0.9826
B)0.9380
C)0.5940
D)0.9975

Question 48

An environmental scientist obtains a sample of water from an irrigation canal thatcontains a certain type of bacteria at a concentration of 3 per milliliter. What is theprobability that there will be exactly 9 bacteria in a 4-milliliter sample?

A)0.9345
B)0.0874
C)0.0655
D)0.0027

Question 49

Last year, a manufacturer produced 700,000 DVD players. Of these, approximately 9%were defective. Assume that a simple random sample of n = 160 players is drawn. Usethe Poisson approximation to the binomial distribution to compute the probability thatexactly twenty of the 160 DVD players were defective.

A)0.0231
B)0.0337
C)0.1250
D)0.0468

Question 50

Last year, a manufacturer produced 2,000,000 DVD players. Of these, approximately 3%were defective. Assume that a simple random sample of n = 200 players is drawn. Usethe Poisson approximation to the binomial distribution to compute the probability thatfewer than four of the 200 DVD players were defective.

A)0.0892
B)0.0620
C)0.1512
D)0.1487

Question 51

The number of typographical errors in a document follows a Poisson distribution with a mean of 4 errors per page. Let X represent the number of errors on 2 pages. Find

A) 2.8
B) 8
C) 4
D) 3.8

Question 52

The number of typographical errors in a document follows a Poisson distribution with a mean of 3 errors per page. Let X represent the number of errors on 4 pages. Find

A) 3
B) 12
C) 13
D) 3.5