Deck 5: Normal Probability Distributions

Question 1

Find the area under the standard normal curve to the left of z = 1.25.

A)0.8944
B)0.1056
C)0.2318
D)0.7682

Answer 1

0.8944

Question 2

Find the area under the standard normal curve between z = -1.5 and z = 2.5.

A)0.9270
B)0.7182
C)0.6312
D)0.9831

Answer 2

0.9270

Question 3

Find the area of the indicated region under the standard normal curve.

A)0.6562
B)1.309
C)0.3438
D)0.309

Answer 3

0.6562

Question 4

Find the area of the indicated region under the standard normal curve.

A)0.0968
B)0.9032
C)0.4032
D)0.0823

Question 5

Find the area under the standard normal curve to the right of z = 1.

A)0.1587
B)0.8413
C)0.1397
D)0.5398

Question 6

Find the area under the standard normal curve between z = 1 and z = 2.

A)0.1359
B)0.8413
C)0.5398
D)0.2139

Question 7

Find the area under the standard normal curve between z = -1.25 and z = 1.25.

A)0.7888
B)0.8817
C)0.6412
D)0.2112

Question 8

Find the area under the standard normal curve between z = 0 and z = 3.

A)0.4987
B)0.9987
C)0.0010
D)0.4641

Question 9

Find the area under the standard normal curve to the right of z = -1.25.

A)0.8944
B)0.5843
C)0.6978
D)0.7193

Question 10

Find the area of the indicated region under the standard normal curve.

A)0.9032
B)0.0968
C)0.0823
D)0.9177

Question 11

Determine whether the graph could represent a variable with a normal distribution. Explain your reasoning.

A)No, the graph crosses the x-axis.
B)No, the graph is skewed right.
C)No, the graph is not symmetric.
D)Yes, the graph fulfills the properties of the normal distribution.

Question 12

Determine whether the graph could represent a variable with a normal distribution. Explain your reasoning.

A)Yes, the graph fulfills the properties of the normal distribution
B)No, the graph is skewed left.
C)No, the graph crosses the x-axis.
D)No, the graph is not symmetric.

Question 13

Find the area under the standard normal curve to the left of z = 1.5.

A)0.9332
B)0.0668
C)0.5199
D)0.7612

Question 14

Find the sum of the areas under the standard normal curve to the left of z = -1.25 and to the right of z = 1.25.

A)0.2112
B)0.7888
C)0.1056
D)0.3944

Question 15

The ACT is an exam used by colleges and universities to evaluate undergraduate applicants. The test scores are
normally distributed. In a recent year, the mean test score was 22.2 and the standard deviation was 4.9. The test
scores of four students selected at random are 16, 24, 9, and 35.
a)Find the z-scores that correspond to each value.
b)Determine whether any of the values are unusual.

Question 16

Find the area under the standard normal curve between z = 1.5 and z = 2.5.

A)0.0606
B)0.9938
C)0.9332
D)0.9816

Question 17

Determine whether the graph could represent a variable with a normal distribution. Explain your reasoning.

A)No, the graph is skewed right.
B)No, the graph crosses the x-axis.
C)No, the graph is skewed left.
D)Yes, the graph fulfills the properties of the normal distribution

Question 18

You are performing a study about the weight of preschoolers. A previous study found the weights to be
normally distributed with a mean of 30 and a standard deviation of 4. You randomly sample 30 preschool
children and find their weights to be as follows. a)Draw a histogram to display these data. Use seven classes. Do the weights appear to be normally
distributed? Explain.
b)Find the mean and standard deviation of your sample.
c)Is there a high probability that the mean and standard deviation of your sample are consistent
with those found in previous studies? Explain your reasoning.

Question 19

Find the area of the indicated region under the standard normal curve.

A)0.1504
B)0.1292
C)0.8489
D)0.0212

Question 20

The SAT is an exam used by colleges and universities to evaluate undergraduate applicants. The test scores are
normally distributed. In a recent year, the mean test score was 1475 and the standard deviation was 308. The
test scores of four students selected at random are 1930, 1340, 2150, and 1450.
a)Find the z-scores that correspond to each value
b)Determine whether any of the values are unusual.

Question 21

Find the probability of z occurring in the indicated region.

A)0.0401
B)0.0668
C)0.9599
D)0.0228

Question 22

Use the standard normal distribution to find $\mathrm { P } ( 0 < \mathrm { z } < 2.25 )$ 2.25).

A)0.4878
B)0.5122
C)0.8817
D)0.7888

Question 23

For the standard normal curve, find the z-score that corresponds to the third quartile.

A)0.67
B)-0.67
C)0.77
D)-0.23

Question 24

IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. An individualʹs IQ score is found to be 90. Find the z-score corresponding to this value.

A)-0.67
B)0.67
C)1.33
D)-1.33

Question 25

For the standard normal curve, find the z-score that corresponds to the first quartile.

A)-0.67
B)0.67
C)0.77
D)-0.23

Question 26

IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. An individualʹs IQ score is found to be 110. Find the z-score corresponding to this value.

A)0.67
B)-0.67
C)1.33
D)-1.33

Question 27

Use the standard normal distribution to find P( $\mathrm { P } ( - 2.50 < \mathrm { z } < 1.50 )$

A)0.9270
B)0.8822
C)0.6167
D)0.5496

Question 28

Find the probability of z occurring in the indicated region.

A)0.9656
B)0.0344
C)0.9772
D)0.4656

Question 29

Assume that the random variable X is normally distributed, with mean $\mu$ = 60 and standard deviation $\sigma$ = 12. Compute the probability $\mathrm { P } ( \mathrm { X } < 75 )$

A)0.8944
B)0.8849
C)0.1056
D)0.9015

Question 30

For the standard normal curve, find the z-score that corresponds to the first decile.

A)-1.28
B)1.28
C)-2.33
D)0.16

Question 31

Assume that the random variable X is normally distributed, with mean $\mu$ = 80 and standard deviation $\sigma$ = 15. Compute the probability $\mathrm { P } ( X > 92 )$

A)0.2119
B)0.1977
C)0.7881
D)0.2420

Question 32

Use the standard normal distribution to find P(-2.25 < z < 1.25).

A)0.8822
B)0.0122
C)0.4878
D)0.8944

Question 33

Use the standard normal distribution to find P(z < -2.33 or z > 2.33).

A)0.0198
B)0.9802
C)0.7888
D)0.0606

Question 34

Find the probability of z occurring in the indicated region.
3

A)0.9772
B)0.0228
C)0.9544
D)0.0456

Question 35

Use the standard normal distribution to find P( $P ( - 2.25 < z < 0 )$

A)0.4878
B)0.5122
C)0.6831
D)0.0122

Question 36

Assume that the random variable X is normally distributed, with mean $\mu$ = 60 and standard deviation $\sigma$ = 8. Compute the probability $\mathrm { P } ( 38 < \mathrm { X } < 70 )$

A)0.8914
B)0.8819
C)0.8944
D)0.7888

Question 37

IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. An individualʹs IQ score is found to be 120. Find the z-score corresponding to this value.

A)1.33
B)-0.67
C)0.67
D)-1.33

Question 38

Find the probability of z occurring in the indicated region.

A)0.2776
B)0.7224
C)0.2224
D)0.1894

Question 39

Find the probability of z occurring in the indicated region.

A)0.9082
B)0.0918
C)0.9332
D)0.0668

Question 40

Find the probability of z occurring in the indicated region.

A)0.4332
B)0.5668
C)0.0668
D)0.9332

Question 41

The lengths of pregnancies of humans are normally distributed with a mean of 268 days and a standard deviation of 15 days. Find the probability of a pregnancy lasting more than 300 days.

A)0.0166
B)0.9834
C)0.2375
D)0.3189

Question 42

The distribution of cholesterol levels in teenage boys is approximately normal with $\mu$ = 170 and $\sigma$ = 30 (Source: U.S. National Center for Health Statistics). Levels above 200 warrant attention. What percent of teenage boys
Have levels between 170 and 225?

A)3.36%
B)6.06%
C)46.64%
D)56.13%

Question 43

Assume that the heights of women are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. The cheerleaders for a local professional basketball team must be between 65.5 and 68.0
Inches. If a woman is randomly selected, what is the probability that her height is between 65.5 and 68.0
Inches?

A)0.1844
B)0.9608
C)0.7881
D)0.3112

Question 44

The distribution of cholesterol levels in teenage boys is approximately normal with $\mu$ = 170 and $\sigma$ = 30 (Source: U.S. National Center for Health Statistics). Levels above 200 warrant attention. Find the probability that a
Teenage boy has a cholesterol level greater than 200.

A)0.1587
B)0.8413
C)0.3419
D)0.2138

Question 45

Assume that the salaries of elementary school teachers in the United States are normally distributed with a mean of $32,000 and a standard deviation of $3000. If a teacher is selected at random, find the probability that
He or she makes more than $36,000.

A)0.0918
B)0.9082
C)0.1056
D)0.4040

Question 46

Assume that the salaries of elementary school teachers in the United States are normally distributed with a mean of $32,000 and a standard deviation of $3000. If a teacher is selected at random, find the probability that
He or she makes less than $28,000.

A)0.0918
B)0.9981
C)0.2113
D)0.9827

Question 47

An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with $\mu$ = 15.5 and $\sigma$ = 3.6. What is the probability that during a given
Week the airline will lose less than 20 suitcases?

A)0.8944
B)0.3944
C)0.1056
D)0.4040

Question 48

The graph depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the probability that a member selected at random is from the shaded area of the
Graph.

A)0.7938
B)0.7745
C)0.7303
D)0.7619

Question 49

The lengths of pregnancies of humans are normally distributed with a mean of 268 days and a standard deviation of 15 days. A baby is premature if it is born three weeks early. What percent of babies are born
Prematurely?

A)8.08%
B)6.81%
C)9.21%
D)10.31%

Question 50

Assume that the heights of women are normally distributed with a mean of 63.6 inches and a standard
deviation of 2.5 inches. The U.S. Army requires that the heights of women be between 58 and 80 inches. If a
woman is randomly selected, what is the probability that her height is between 58 and 80 inches?

Question 51

IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the IQ score that corresponds to a z-score of 1.96.

A)129.4
B)115.6
C)122.4
D)132.1

Question 52

An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with $\mu$ = 15.5 and $\sigma$ = 3.6. What is the probability that during a given
Week the airline will lose between 10 and 20 suitcases?

A)0.8314
B)0.3944
C)0.1056
D)0.4040

Question 53

The lengths of pregnancies of humans are normally distributed with a mean of 268 days and a standard deviation of 15 days. Find the probability of a pregnancy lasting less than 250 days.

A)0.1151
B)0.1591
C)0.0606
D)0.0066

Question 54

The distribution of cholesterol levels in teenage boys is approximately normal with $\mu$ = 170 and $\sigma$ = 30 (Source: U.S. National Center for Health Statistics). Levels above 200 warrant attention. Find the probability that a
Teenage boy has a cholesterol level greater than 225.

A)0.0336
B)0.0606
C)0.0718
D)0.0012

Question 55

Assume that the heights of American men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. The U.S. Marine Corps requires that men have heights between 64 and 78 inches. Find
The percent of men meeting these height requirements.

A)96.26%
B)3.67%
C)99.93%
D)31.12%

Question 56

An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with $\mu$ = 15.5 and $\sigma$ = 3.6. What is the probability that during a given
Week the airline will lose more than 20 suitcases?

A)0.1056
B)0.3944
C)0.4040
D)0.8944

Question 57

Assume that blood pressure readings are normally distributed with $\mu$ = 120 and $\sigma$ = 8. A blood pressure reading of 145 or more may require medical attention. What percent of people have a blood pressure reading
Greater than 145?

A)0.09%
B)99.91%
C)6.06%
D)11.09%

Question 58

IQ test scores are normally distributed with a mean of 105 and a standard deviation of 11. An individualʹs IQ score is found to be 119. Find the z-score corresponding to this value.

A)1.27
B)-1.27
C)0.79
D)-0.79

Question 59

IQ test scores are normally distributed with a mean of 104 and a standard deviation of 15. An individualʹs IQ score is found to be 111. Find the z-score corresponding to this value.

A)0.47
B)-0.47
C)2.14
D)-2.14

Question 60

The graph depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the probability that a member selected at random is from the shaded area of the
Graph.

A)0.7486
B)0.4400
C)0.6293
D)0.8051

Question 61

Find the z-score for which 99% of the distributionʹs area lies between -z and z.

A)(-2.575, 2.575)
B)(-1.645, 1.645)
C)(-2.33, 2.33)
D)(-1.28, 1.28)

Question 62

Find the z-score that has 84.85% of the distributionʹs area to its right.

A)-1.03
B)1.03
C)-0.39
D)0.39

Question 63

Use a standard normal table to find the z-score that corresponds to the $80 ^ { \text {th } }$ percentile.

A)0.84
B)1.405
C)2.41
D)0.2

Question 64

Provide an appropriate response. Use the Standard Normal Table to find the probability.
The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15
days. Out of 50 pregnancies, how many would you expect to last less than 250 days?

Question 65

For the standard normal curve, find the z-score that corresponds to the $30 ^ { \text {th } }$ percentile.

A)-0.53
B)-0.98
C)-0.47
D)-0.12

Question 66

Find the z-score that corresponds to the given area under the standard normal curve.

Question 67

For the standard normal curve, find the z-score that corresponds to the $90 ^ { \text {th } }$ percentile.

A)1.28
B)0.28
C)1.52
D)2.81

Question 68

Provide an appropriate response. Use the Standard Normal Table to find the probability.
An airline knows from experience that the distribution of the number of suitcases that get lost each week on a
certain route is approximately normal with = 15.5 and = 3.6. In one year, how many weeks would you
expect the airline to lose between 10 and 20 suitcases?

Question 69

Provide an appropriate response. Use the Standard Normal Table to find the probability.
Assume that the heights of women are normally distributed with a mean of 63.6 inches and a standard
deviation of 2.5 inches. The U.S. Army requires that the heights of women be between 58 and 80 inches. If 200
women want to enlist in the U.S. Army, how many would you expect to meet the height requirements?

Question 70

Find the z-score for which 70% of the distributionʹs area lies to its right.

A)-0.53
B)-0.98
C)-0.81
D)-0.47

Question 71

For the standard normal curve, find the z-score that corresponds to the $7 ^ { \text {th } }$ decile.

A)0.53
B)0.98
C)0.47
D)0.12

Question 72

Find the z-score that corresponds to the given area under the standard normal curve.

Question 73

Provide an appropriate response. Use the Standard Normal Table to find the probability.
Assume that the heights of men are normally distributed with a mean of 69.0 inches and a standard deviation
of 2.8 inches. The U.S. Marine Corps requires that the heights of men be between 64 and 78 inches. If 500 men
want to enlist in the U.S. Marine Corps, how many would you not expect to meet the height requirements?

Question 74

Provide an appropriate response. Use the Standard Normal Table to find the probability.
The distribution of cholesterol levels in teenage boys is approximately normal with = 170 and = 30. Levels
above 200 warrant attention. If 95 teenage boys are examined, how many would you expect to have cholesterol
levels greater than 225?

Question 75

Find the z-score that is greater than the mean and for which 70% of the distributionʹs area lies to its left.

A)0.53
B)0.98
C)0.81
D)0.47

Question 76

Find the z-score that corresponds to the given area under the standard normal curve.

Question 77

Use a standard normal table to find the z-score that corresponds to the cumulative area of 0.7019.

A)0.53
B)-0.53
C)0.835
D)-0.835

Question 78

Find the z-scores for which 98% of the distributionʹs area lies between -z and z.

A)(-2.33, 2.33)
B)(-1.645, 1.645)
C)(-1.96, 1.96)
D)(-0.99, 0.99)

Question 79

Find the z-score that corresponds to the given area under the standard normal curve.

Question 80

Find the z-scores for which 90% of the distributionʹs area lies between -z and z.

A)(-1.645, 1.645)
B)(-2.33, 2.33)
C)(-1.96, 1.96)
D)(-0.99, 0.99)