Deck 6: Probability

Question 1

What proportion of a normal distribution is located between z = -1.50 and z = +1.50?​

A)​0.9332
B)​0.0668
C)​0.4332
D)​0.8664

Answer 1

​0.8664

Question 2

A vertical line is drawn through a normal distribution at z = 0.50,and separates the distribution into two sections.What proportion of the distribution is in the larger section?​

A)​0.6915
B)​0.3085
C)​0.1915
D)​0.3830

Answer 2

​0.6915

Question 3

What proportion of a normal distribution is located in the tail beyond z = -1.00?​

A)​0.8413
B)​0.1587
C)​-0.3413
D)​-0.1587

Answer 3

​0.1587

Question 4

What z-score value separates the top 70% of a normal distribution from the bottom 30%?​

A)​z = 0.52
B)​z = 0.84
C)​z = -0.52
D)​z = -0.84

Question 5

A vertical line is drawn through a normal distribution at z = 1.20.What proportion of the distribution is on the left-hand side of the line?​

A)​0.8849
B)​0.1151
C)​0.3849
D)​0.7698

Question 6

A jar contains 10 red marbles and 30 blue marbles.What is the probability of randomly selecting a red marble from the jar?​

A)​10/30
B)​10/40
C)​1/10
D)​1/40

Question 7

What proportion of a normal distribution is located between the mean and z = 1.40?​

A)​0.9192
B)​0.0808
C)​0.4192
D)​0.8384

Question 8

Which of the following are requirements of a random sample?​

A)​Every individual has an equal chance of being selected.
B)​The probabilities cannot change during a series of selections.
C)​There must be sampling with replacement.
D)​There must be at least 100 observations.

Question 9

What proportion of a normal distribution is located between the mean and z = -0.40?​

A)​0.6554
B)​0.3446
C)​0.1554
D)​0.3108

Question 10

A vertical line is drawn through a normal distribution at z = 0.80.What proportion of the distribution is on the right-hand side of the line?​

A)​0.7881
B)​0.2119
C)​0.2881
D)​0.5762

Question 11

What z-score values form the boundaries for the middle 60% of a normal distribution?​

A)z = +0.25 and z = -0.25​
B)​z = +0.39 and z = -0.39
C)​z = +0.52 and z = -0.52
D)​z = +0.84 and z = -0.84

Question 12

What is the probability of randomly selecting a z-score less than z = 1.25 from a normal distribution.​

A)​0.8944
B)​0.1056
C)​0.3944
D)​0.2112

Question 13

A jar contains 10 red marbles and 30 blue marbles.A random sample without replacement of n = 3 marbles is selected from the jar.If the first two marbles are both blue,what is the probability that the third marble will be red?​

A)​10/37
B)​10/38
C)​10/40
D)​8/38

Question 14

What proportion of a normal distribution is located in the tail below z = 2.00?​

A)​0.9772
B)​0.0228
C)​0.4772
D)​0.0456

Question 15

A normal distribution has a mean of µ = 40 with σ = 10.What proportion of the scores in this distribution are smaller than X = 35?​

A)​0.3085
B)​0.6915
C)​0.0668
D)​0.9332

Question 16

What is the probability of randomly selecting a z-score greater than z = 0.75 from a normal distribution?​

A)​0.7734
B)​0.2266
C)​0.2734
D)​0.4532

Question 17

A normal distribution has a mean of µ = 40 with σ = 10.What proportion of the scores in this distribution are greater than X = 55?​

A)​0.3085
B)​0.6915
C)​0.0668
D)​0.9332

Question 18

What z-score value separates the top 10% of a normal distribution from the bottom 90%?​

A)​z = 1.28
B)​z = 0.25
C)​z = -1.28
D)​z = -0.25

Question 19

A normal distribution has µ = 80 and σ = 10.What is the probability of randomly selecting a score greater than 90 from this distribution?​

A)​p = 0.8413
B)​p = 0.1587
C)​p = 0.3085
D)​p = 0.6915

Question 20

What proportion of a normal distribution is located between z = -0.25 and z = +0.25?​

A)0.5987​
B)​0.4013
C)​0.0987
D)​0.1974

Question 21

Under what circumstances does the binomial distribution approximate a normal distribution?​

A)​when pn > 10
B)​when qn > 10
C)​when pn and qn are both > 10
D)​when npq > 10

Question 22

A normal distribution has a mean of µ = 70 with σ = 12.If one score is randomly selected from this distribution,what is the probability that the score will be less than X = 76?​

A)​0.1915
B)​0.3085
C)​0.6915
D)​0.3830

Question 23

A normal distribution has a mean of µ = 100 with σ = 20.If one score is randomly selected from this distribution,what is the probability that the score will have a value between X = 80 and X = 100?​

A)​0.8413
B)​0.1587
C)​0.3413
D)​0.6826

Question 24

John drives to work each morning and the trip takes an average of µ = 38 minutes.The distribution of driving times is approximately normal with a standard deviation of σ = 5 minutes.For a randomly selected morning,what is the probability that John's drive to work will take between 36 and 40 minutes?​

A)​0.0793
B)​0.1526
C)​0.1554
D)​0.3108

Question 25

John drives to work each morning and the trip takes an average of µ = 38 minutes.The distribution of driving times is approximately normal with a standard deviation of σ = 5 minutes.For a randomly selected morning,what is the probability that John's drive to work will take less than 35 minutes?​

A)​0.6554
B)​0.3446
C)​0.7257
D)​0.2743

Question 26

A normal distribution has a mean of µ = 70 with σ = 12.If one score is randomly selected from this distribution,what is the probability that the score will be greater than X = 79?​

A)​0.7734
B)​0.2266
C)​0.2734
D)​0.3085

Question 27

A normal distribution has a mean of µ = 70 with σ = 12.If one score is randomly selected from this distribution,what is the probability that the score will be greater than X = 58?​

A)​0.8413
B)​0.1577
C)​0.3413
D)​0.6826

Question 28

A true/false test has 100 questions.Using the normal approximation to the binomial distribution,what is the probability of getting more than 55 correct by just guessing?​

A)​p(X > 55)
B)​p(X > 55.5)
C)​p(X > 54.5)
D)​p(X > 45)

Question 29

A normal distribution has a mean of µ = 70 with σ = 12.If one score is randomly selected from this distribution,what is the probability that the score will be less than X = 55?​

A)​0.3944
B)​0.1056
C)​0.8944
D)​0.7888

Question 30

A normal distribution has a mean of µ = 80 with σ = 20.What score separates the lowest 30% of the distribution from the rest of the scores?​

A)X = 90.4​
B)​X = 69.6
C)​X = 110
D)​X = 50

Question 31

A normal distribution has a mean of µ = 80 with σ = 20.What score separates the highest 15% of the distribution from the rest of the scores?​

A)X = 59.2​
B)​X = 100.8
C)​X = 95
D)​X = 65

Question 32

A binomial distribution has p = 1/5 and q = 4/5 with n = 100.In the normal approximation to this distribution,what is the z-score corresponding to X = 25?​

A)​z = 0.50
B)​z = 1.00
C)​z = 1.25
D)​z = 1.50

Question 33

For a binomial distribution with p = q = 1/2 and n = 36,what is the mean for the normal approximation?​

A)​3
B)​9
C)​16
D)​18

Question 34

A true/false test has 100 questions.Using the normal approximation to the binomial distribution,what is the probability of getting 55 or more correct by just guessing?​

A)​p(X > 55)
B)​p(X > 55.5)
C)​p(X > 54.5)
D)​p(X > 45)

Question 35

A normal distribution has a mean of µ = 24 with σ = 3.What is the minimum score needed to be in the top 14% of the distribution?​

A)​X = 20.76
B)​X = 27.24
C)​X = 25.08
D)​X = 24.42

Question 36

Scores on the SAT form a normal distribution with a mean of µ = 500 with σ = 100.If the state college only accepts students who score in the top 60% on the SAT,what is the minimum score needed to be accepted?​

A)X = 475​
B)​X = 525
C)​X = 440
D)​X = 560

Question 37

A normal distribution has a mean of µ = 100 with σ = 20.If one score is randomly selected from this distribution,what is the probability that the score will have a value between X = 90 and X = 110?​

A)0.6915​
B)​0.3085
C)​0.1915
D)​0.3830

Question 38

A multiple-choice test with 48 questions has four choices for each question.What is the probability of getting more than 12 questions correct by just guessing?​

A)​0.5000
B)​0.4325
C)​0.5675
D)​0.0675

Question 39

A normal distribution has a mean of µ = 100 with σ = 20.If one score is randomly selected from this distribution,what is the probability that the score will have a value between X = 90 and X = 120?​

A)0.1498​
B)​0.4672
C)​0.5328
D)​0.2996

Question 40

A normal distribution has a mean of µ = 80 with σ = 20.What score separates the highest 40% of the distribution from the rest of the scores?​

A)​X = 75
B)​X = 85
C)​X = 54.4
D)​X = 105.6

Question 41

For any normal distribution,exactly 97.50% of the z-score values are less than z = 1.96.

Question 42

For a normal distribution,the proportion located between z = -1.00 and z = +1.00 is p = 34.13%.

Question 43

If one score is randomly selected from a normal distribution with µ = 100 and σ = 20,the probability of obtaining a score less than X = 95 is p = 0.4013.

Question 44

For a population with a mean of µ = 80 and σ = 10,only 2.28% of the scores are greater than X = 100.

Question 45

All probabilities can be expressed as decimal values ranging from 0 to 1.00.

Question 46

A vertical line is drawn through a normal distribution dividing the distribution into two parts.If the smaller part equals 0.1915 of the distribution,then the line was drawn at z = 0.50 or at z = -0.50.

Question 47

A jar contains 10 red marbles and 20 blue marbles.If you take a random sample with replacement of two marbles from this jar and the first marble is blue,then the probability that the second marble is blue is p = 19/29.

Question 48

If one score is randomly selected from a normal distribution with µ = 100 and σ = 20,the probability of obtaining a score greater than X = 110 is p = 0.6915.

Question 49

For a normal distribution,the proportion in the tail below z = -2.00 is equal to 0.0228.

Question 50

For a normal distribution,proportions in the right-hand tail are positive and proportions in the left-hand tail are negative.

Question 51

For a normal distribution,the proportion in the tail beyond z = 1.50 is p = 0.0668.

Question 52

For a normal distribution with µ = 100 and σ = 20,the score that separates the top 60% of the distribution from the bottom 40% is X = 95.

Question 53

When the z-score value in a normal distribution is negative,the majority of the area is on the right-hand side of the distribution.

Question 54

A vertical line drawn through a normal distribution at z = -0.75 will separate the distribution into two sections.The proportion in the smaller section is 0.2734.

Question 55

For a normal distribution,the z-score boundary that separates the lowest 2.5% of the scores from the rest is z = -1.96.

Question 56

For any normal distribution,the proportion located between the mean and z = 1.40 is 0.9192.

Question 57

For a normal distribution with µ = 80 and σ = 10 the score that separates the bottom 10% of the distribution from the rest is 67.2.

Question 58

A vertical line drawn through a normal distribution at z = 1.25 will separate the distribution into two sections.The proportion in the smaller section is 0.1056.

Question 59

For any normal distribution,the proportion in the tail above z = 2.00 is p = 0.0228.

Question 60

A vertical line drawn through a normal distribution at z = -0.80 will separate the distribution into two sections.The proportion in the larger section is 7881.​

Question 61

For the normal approximation to the binomial distribution with n = 100 and p = 1/5,the probability of selecting a score greater than or equal to 25 is p = 0.1056.

Question 62

If one score is randomly selected from a normal distribution with µ = 100 and σ = 20,the probability of obtaining a score less than X = 70 is p = 0.0013.

Question 63

A normal distribution has a mean of µ = 100 with σ = 20.Find the following probabilities:
a. p(X > 102)
b. p(X < 65)
c. p(X < 130)
d. p(95 < X < 105)

Question 64

Assume that the total score (from both teams)for college football games averages µ = 42 points per game,and that the distribution of total points is approximately normal with σ = 20.
a. What is the probability that a randomly selected game would have more than 60 points?
b. What proportion of college football games have a point total between 20 and 60?

Question 65

Assume that a vertical line is drawn through a normal distribution at each of the following z-score locations.In each case,determine whether the tail is on the left side or the right side of the line and find the proportion of the distribution that is located in the tail.
a. z = +1.80
b. z = +0.60
c. z = -0.40
d. z = -1.25

Question 66

If one score is randomly selected from a normal distribution with µ = 100 and σ = 20,the probability of obtaining a score between X = 80 and X = 120 is p = 0.3413.

Question 67

For a normal distribution,
a. What z-score separates the highest 10% from the rest of the scores?
b. What z-score separates the highest 30% from the rest of the scores?
c. What z-score separates the lowest 40% from the rest of the scores?
d. What z-score separates the lowest 20% from the rest of the scores?

Question 68

For the normal approximation to the binomial distribution with n = 100 and p = 1/2,a score of X = 60 corresponds to a z-score of z = 2.00.

Question 69

If one score is randomly selected from a normal distribution with µ = 100 and σ = 20,the probability of obtaining a score between X = 90 and X = 100 is p = 0.3085.

Question 70

The binomial distribution for p = 1/2 and n = 100 has a standard deviation of σ = 25.

Question 71

For a normal distribution with µ = 200 and σ = 50,find the following values:
a. What X value separates the highest 10% of the distribution from the rest of the scores?
b. What X values form the boundaries for the middle 60% of the distribution?
c. What is the probability of randomly selecting a score greater than X = 325?

Question 72

A binomial distribution with p = 2/3 and n = 24 meets the criterion for using the normal approximation.

Question 73

The binomial distribution for p = 1/4 and n = 96 has a mean of μ = 24.

Question 74

For a binomial distribution,the probability of obtaining a score of X = 19 or greater is computed as p(X > 18.5).​

Question 75

In an ESP experiment subjects must predict whether a number randomly generated by a computer will be odd or even.
a. What is the probability that a subject would guess exactly 18 correct in a series of 36 trials?
b. What is the probability that a subject would guess more than 20 correct in a series of 36 trials?

Question 76

For a binomial distribution,the probability of obtaining a score greater than 19 is computed as p(X > 19.5).