Deck 7: The Normal Distribution

Question 1

Find the z-scores that bound the middle 60% of the area under the standard normal curve.

A) -0.84, 0.84
B) -1.02, 1.02
C) -0.97, 0.97
D) -0.78, 0.78

Answer 1

-0.84, 0.84

Question 2

A normal population has a mean and standard deviation What is the probability that a randomly chosen value will be greater than 36?

A) 0.8485
B) 0.7257
C) 0.1210
D) 0.8790

Answer 2

0.1210

Question 3

A normal population has a mean and standard deviation What proportion of the population is less than 39?

A) 0.2743
B) 0.8106
C) 1.0000
D) 0.7257

Answer 3

0.7257

Question 4

Find the shaded area under the standard normal curve.

A) 0.3867
B) 0.2734
C) 0.2266
D) 0.7734

Question 5

Find the shaded area under the standard normal curve.

A) 0.8944
B) 0.0528
C) 0.3944
D) 0.1056

Question 6

Find the area under the standard normal curve to the right of z = 1.6.

A) 0.4452
B) 0.0548
C) 0.9452
D) 0.0274

Question 7

Find the area under the standard normal curve that lies outside the interval between z = -1.4 and z = -0.5.

A) 0.2278
B) 0.1915
C) 0.7722
D) 0.8085

Question 8

The following figure is a probability density curve that represents the lifetime, in months, of a certain type of laptop battery. Find the proportion of batteries with lifetimes between 10 and 20 months.

A) 0.34
B) 0.09
C) 0.66
D) 0.25

Question 9

Find the z-score for which the area to the right is 0.92.

A) -1.22
B) -1.68
C) -1.60
D) -1.41

Question 10

Use technology to solve the following problem: A normal population has a mean and standard deviation What proportion of the population is less than 41?

A) 0.8275
B) 0.7625
C) 0.2375
D) 1.0000

Question 11

The following figure is a probability density curve that represents the lifetime, in months, of a certain type of laptop battery. Find the proportion of batteries with lifetimes less than 20 months.

A) 0.26
B) 0.20
C) 0.8
D) 0.06

Question 12

Find the shaded area under the standard normal curve.

A) 0.8291
B) 0.4878
C) 0.0854
D) 0.1709

Question 13

Find the z-score for which the area to the left is 0.79.

A) 0.58
B) 0.64
C) 0.81
D) 1.04

Question 14

The following figure is a probability density curve that represents the lifetime, in months, of a certain type of laptop battery. What is the probability that a randomly chosen battery lasts longer than 20 months?

A) 0.51
B) 0.25
C) 0.49
D) 0.24

Question 15

Find the area under the standard normal curve that lies between z = 0.5 and z = 2.8.

A) 0.5026
B) 0.6940
C) 0.3060
D) 0.4974

Question 16

Find the shaded area under the standard normal curve.

A) 0.5000
B) 0.6056
C) 0.3944
D) 0.1972

Question 17

Compact fluorescent bulbs are more energy-efficient than incandescent bulbs, but they take longer to reach full brightness. The time it takes for a compact fluorescent bulb to reach full brightness is normally distributed with mean 29.9 seconds and standard deviation 4.9 seconds. Find and interpret the z-score for x=26.1.

A) z=0.71: the time to reach full brightness is 0.71 standard deviations above the mean.
B) z=0.71: the time to reach full brightness is 0.71 standard deviations below the mean.
C) z=-0.78 : the time to reach full brightness is 0.78 standard deviations below the mean.
D) z=-0.78: the time to reach full brightness is 0.78 standard deviations above the mean.

Question 18

Find the area under the standard normal curve to the left of z = 0.8.

A) 0.2881
B) 0.2119
C) 0.7881
D) 0.3941

Question 19

A normal distribution has mean μ = 16 and standard deviation σ = 3. Find and interpret the z-score for x = 13.

A) z = -3: a value of 13 is one standard deviation below the mean.
B) z = 19: a value of 13 is one standard deviation above the mean.
C) z = 1: a value of 13 is one standard deviation above the mean.
D) z = -1: a value of 13 is one standard deviation below the mean.

Question 20

A normal distribution has mean =60 and standard deviation =20 . Find and interpret the z-score for x=90.

A) z=-1.50 : a value of 90 is 1.50 standard deviations below the mean.
B) z=10 : a value of 90 is 10 standard deviations below the mean.
C) z=1.50 : a value of 90 is 1.50 standard deviations above the mean.
D) z=2.25 : a value of 90 is 2.25 standard deviations above the mean.

Question 21

Use technology to solve the following problem: A bottler of drinking water fills plastic bottles with a mean volume of 1,000 milliliters (mL) and standard deviation 7 mL. The fill volumes are normally
Distributed. What proportion of bottles have volumes greater than 1,002 mL?

A) 1.0000
B) 0.9568
C) 0.6575
D) 0.3875

Question 22

Use technology to solve the following problem: A recent study reported that diastolic blood pressures of adult women in the United States are approximately normally distributed with mean
80)8 and standard deviation 9.2. What proportion of women have blood pressures between 70.4 and
83)4?

A) 0.4821
B) 1.4130
C) 0.7404
D) 0.5179

Question 23

Use technology to solve the following problem: A bottler of drinking water fills plastic bottles with a mean volume of 1,002 milliliters (mL) and standard deviation 4 mL. The fill volumes are normally
Distributed. What proportion of bottles have volumes less than 1,002 mL?

A) 0.5517
B) 1.0000
C) 0.5000
D) 0.9987

Question 24

The weights of 6-week-old poults (juvenile turkeys) are normally distributed with a mean 9.0 pounds and standard deviation 2.5 pound(s). Find the 75th percentile of the weights.

A) 11.74 lb
B) 10.67 lb
C) 8.54 lb
D) 9.60 lb

Question 25

A recent study reported that diastolic blood pressures of adult women in the United States are approximately normally distributed with mean 80.1 and standard deviation 9.5. What proportion of
Women have blood pressures lower than 67.9?

A) 0.0501
B) 0.9499
C) 0.8997
D) 0.1003

Question 26

A bottler of drinking water fills plastic bottles with a mean volume of 1,007 milliliters (mL) and standard deviation 6 mL. The fill volumes are normally distributed. What proportion of bottles have
Volumes less than 1,015 mL?

A) 1.0000
B) 0.9082
C) 0.6293
D) 0.9251

Question 27

A bottler of drinking water fills plastic bottles with a mean volume of 998 milliliters (mL) and standard deviation 7 mL. The fill volumes are normally distributed. What proportion of bottles have
Volumes between 988 mL and 991 mL?

A) 0.0764
B) 0.4549
C) 0.0823
D) 0.1587

Question 28

Use technology to solve the following problem: A normal population has a mean and standard deviation What proportion of the population is between 18 and 26?

A) 0.3217
B) 0.0478
C) 0.6783
D) 0.3694

Question 29

A normal population has a mean and standard deviation . What proportion of the population is between 23 and 32?

A) 0.6306
B) 0.2177
C) 0.3694
D) 0.5871

Question 30

Use technology to solve the following problem: A recent study reported that diastolic blood pressures of adult women in the United States are approximately normally distributed with mean
80)9 and standard deviation 8.8. What proportion of women have blood pressures lower than 65.8?

A) 0.9569
B) 0.9785
C) 0.0431
D) 0.0215

Question 31

A bottler of drinking water fills plastic bottles with a mean volume of 1,006 milliliters (mL) and standard deviation 6 mL. The fill volumes are normally distributed. What proportion of bottles have
Volumes greater than 1,009 mL?

A) 1.0000
B) 0.9998
C) 0.6331
D) 0.3085

Question 32

Use technology to solve the following problem: A normal population has a mean and standard deviation What is the probability that a randomly chosen value will be greater than
18?

A) 0.9684
B) 0.6386
C) 0.9088
D) 0.0316

Question 33

Use technology to solve the following problem: A normal population has a mean and standard deviation What is the 58th percentile of the population?

A) 29.60
B) 26.64
C) 32.56
D) 35.52

Question 34

Use technology to solve the following problem: A recent study reported that diastolic blood pressures of adult women in the United States are approximately normally distributed with mean
80)6 and standard deviation 9.9. What proportion of women have blood pressures higher than 85.8?

A) 0.7003
B) 0.3501
C) 0.6499
D) 0.2997

Question 35

A normal population has a mean and standard deviation . What is the 43rd percentile of the population?

A) 15.00
B) 12.28
C) 16.37
D) 13.64

Question 36

A recent study reported that diastolic blood pressures of adult women in the United States are approximately normally distributed with mean 80.3 and standard deviation 8.6. What proportion of
Women have blood pressures between 88.1 and 89.4?

A) 0.9632
B) 0.0368
C) 1.6740
D) 0.1500

Question 37

A recent study reported that diastolic blood pressures of adult women in the United States are approximately normally distributed with mean 80.3 and standard deviation 8.9. What proportion of
Women have blood pressures higher than 85.8?

A) 0.3662
B) 0.7324
C) 0.2676
D) 0.6338

Question 38

The weights of 6-week-old poults (juvenile turkeys) are normally distributed with a mean 8.5 pounds and standard deviation 1.4 pounds. Find the first quartile of the weight.

A) 6.05 lb
B) 9.07 lb
C) 6.80 lb
D) 7.56 lb

Question 39

Use technology to solve the following problem: A bottler of drinking water fills plastic bottles with a mean volume of 990 milliliters (mL) and standard deviation 7 mL. The fill volumes are normally
Distributed. What proportion of bottles have volumes between 985 mL and 988 mL?

A) 0.3875
B) 0.2375
C) 0.3603
D) 0.1500

Question 40

Use technology to solve the following problem: The weights of 6-week-old poults (juvenile turkeys) are normally distributed with a mean 8.7 pounds and standard deviation 2.0 pound(s). Find the 84th
Percentile of the weights.

A) 10.68 lb
B) 12.82 lb
C) 8.54 lb
D) 11.75 lb

Question 41

Use technology to solve the following problem: A sample of size 70 will be drawn from a population with mean 25 and standard deviation 11. Find the probability that will be between 23
And 26.

A) 0.2234
B) 0.0641
C) 0.6789
D) 0.7124

Question 42

A sample of size 50 will be drawn from a population with mean 73 and standard deviation 8. Find the 19th percentile of

A) 73.8
B) 75.8
C) 72.0
D) 75.7

Question 43

The lifetime of a certain type of automobile tire (in thousands of miles) is normally distributed with mean and standard deviation . What proportion of tires have lifetimes of less than 42
Thousand miles?

A) 0.3070
B) 0.6930
C) 0.3859
D) 0.6141

Question 44

Use technology to solve the following problem: The weights of 6-week-old poults (juvenile turkeys) are normally distributed with a mean 9.1 pounds and standard deviation 2.4 pounds. A turkey farmer
Wants to provide a money-back guarantee that her 6-week poults will weigh at least a certain
Amount. What weight should she guarantee so that she will have to give her customer's money back
Only 1% of the time?

A) 3.51 lb
B) 2.81 lb
C) 3.86 lb
D) 3.16 lb

Question 45

The lifetime of a certain type of automobile tire (in thousands of miles) is normally distributed with mean and standard deviation . What proportion of tires have lifetimes between 40 and
50 thousand miles?

A) 0.6450
B) 2.0000
C) 0.3550
D) 1.1935

Question 46

A sample of size 85 will be drawn from a population with mean 20 and standard deviation 8. Find the probability that will be between 19 and 22.

A) 0.8256
B) 0.8642
C) 0.0107
D) 0.1251

Question 47

According to a recent study, the weight of male babies less than two months old in the United States is normally distributed with mean 11.4 pounds and standard deviation 2.8 pounds. What proportion
Of babies weigh between 10.3 and 12.5 pounds?

A) 0.6965
B) 0.3035
C) 1.0000
D) 0.7800

Question 48

Use technology to solve the following problem: According to a recent study, the weight of male babies less than two months old in the United States is normally distributed with mean 12.0 pounds
And standard deviation 2.6 pounds. What proportion of babies weigh less than 10.3 pounds?

A) 0.8717
B) 0.7434
C) 0.1283
D) 0.2566

Question 49

Use technology to solve the following problem: According to a recent study, the weight of male babies less than two months old in the United States is normally distributed with mean 11.4 pounds
And standard deviation 2.7 pounds. What proportion of babies weigh between 9.7 and 11.5 pounds?

A) 0.6667
B) 0.7497
C) 0.2503
D) 0.7792

Question 50

Use technology to solve the following problem: The lifetime of a certain type of automobile tire (in thousands of miles) is normally distributed with mean and standard deviation . What
Proportion of tires have lifetimes greater than 32 thousand miles?

A) 0.9544
B) 0.9088
C) 0.0456
D) 0.0912

Question 51

According to a recent study, the weight of male babies less than two months old in the United States is normally distributed with mean 12.0 pounds and standard deviation 2.4 pounds. What proportion
Of babies weigh less than 9.1 pounds?

A) 0.9434
B) 0.0566
C) 0.1131
D) 0.8869

Question 52

According to a recent study, the weight of male babies less than two months old in the United States is normally distributed with mean 11.9 pounds and standard deviation 2.6 pounds. What proportion
Of babies weigh more than 10.1 pounds?

A) 0.7549
B) 0.2451
C) 0.8775
D) 0.1225

Question 53

The weights of 6-week-old poults (juvenile turkeys) are normally distributed with a mean 9.0 pounds and standard deviation 2.4 pounds. A turkey farmer wants to provide a money-back
Guarantee that her 6-week poults will weigh at least a certain amount. What weight should she
Guarantee so that she will have to give her customer's money back only 1% of the time?

A) 3.41 lb
B) 3.07 lb
C) 2.73 lb
D) 4.09 lb

Question 54

The lifetime of a certain type of automobile tire (in thousands of miles) is normally distributed with mean and standard deviation . What proportion of tires have lifetimes greater than 48
Thousand miles?

A) 0.4666
B) 0.0668
C) 0.5334
D) 0.9332

Question 55

Use technology to solve the following problem: The weights of 6-week-old poults (juvenile turkeys) are normally distributed with a mean 8.8 pounds and standard deviation 1.8 pounds. Find the first
Quartile of the weight.

A) 6.07 lb
B) 6.83 lb
C) 9.11 lb
D) 7.59 lb

Question 56

Use technology to solve the following problem: The lifetime of a certain type of automobile tire (in thousands of miles) is normally distributed with mean and standard deviation . What
Proportion of tires have lifetimes of less than 49 thousand miles?

A) 0.1056
B) 0.4472
C) 0.8944
D) 0.5528

Question 57

Use technology to solve the following problem: According to a recent study, the weight of male babies less than two months old in the United States is normally distributed with mean 11.0 pounds
And standard deviation 2.4 pounds. What proportion of babies weigh more than 11.7 pounds?

A) 0.3853
B) 0.3074
C) 0.6926
D) 0.6147

Question 58

A sample of size 39 will be drawn from a population with mean 15 and standard deviation 6. Find the probability that will be greater than 16.

A) 0.1271
B) 0.1170
C) 0.1492
D) 0.8508

Question 59

Use technology to solve the following problem: The lifetime of a certain type of automobile tire (in thousands of miles) is normally distributed with mean and standard deviation . What
Proportion of tires have lifetimes between 33 and 48 thousand miles?

A) 1.1980
B) 0.7742
C) 3.0000
D) 0.2258

Question 60

Use technology to solve the following problem: A sample of size 45 will be drawn from a population with mean 94 and standard deviation 14. Find the 32nd percentile of

A) 97.7
B) 93.0
C) 95.4
D) 91.2

Question 61

A survey reported that in a recent year, the mean serum cholesterol level in milligrams per deciliter for U.S. adults was 203 with a standard deviation of 39. A random sample of 102 adults was
Chosen. What is the probability that the mean cholesterol level is between 199 and 208?

A) 0.7523
B) 0.2477
C) 0.9015
D) 1.2900

Question 62

Use technology to solve the following problem: The mean number of pets per household is 3.03 with standard deviation 1.5. A sample of 56 households is drawn. Find the 62nd percentile of the
Sample mean.

A) 3.95
B) 2.57
C) 3.09
D) 3.65

Question 63

Use technology to solve the following problem: A certain car model has a mean gas mileage of 29 miles per gallon (mpg) with a standard deviation 5 mpg. A pizza delivery company buys 40 of these
Cars. What is the probability that the average mileage of the fleet is greater than 27.8 mpg?

A) 0.9655
B) 0.9355
C) 0.0345
D) 0.9062

Question 64

A certain car model has a mean gas mileage of 28 miles per gallon (mpg) with a standard deviation 3 mpg. A pizza delivery company buys 43 of these cars. What is the probability that the average
Mileage of the fleet is greater than 27.6 mpg?

A) 0.9147
B) 0.8078
C) 0.0853
D) 0.6808

Question 65

Use technology to solve the following problem: A survey reported that in a recent year, the mean serum cholesterol level in milligrams per deciliter for U.S. adults was 198 with a standard deviation
Of 36. A random sample of 114 adults was chosen. What is the probability that the mean
Cholesterol level is less than 194?

A) 0.4558
B) 0.5442
C) 0.1177
D) 0.8823

Question 66

Use technology to solve the following problem: A sample of size 51 will be drawn from a population with mean 11 and standard deviation 7. Find the probability that will be less than 12.

A) 0.8106
B) 0.8462
C) 0.8390
D) 0.1538

Question 67

A sample of size 56 will be drawn from a population with mean 26 and standard deviation 11. Find the probability that will be less than 28.

A) 0.9131
B) 0.0869
C) 0.9394
D) 0.9406

Question 68

The mean annual income for people in a certain city (in thousands of dollars) is 46, with a standard deviation of 33. A pollster draws a sample of 55 people to interview. What is the probability that the
Sample mean income is between 42 and 50 (thousands of dollars)?

A) 0.3681
B) 0.6319
C) 0.1841
D) 0.8159

Question 69

A survey reported that in a recent year, the mean serum cholesterol level in milligrams per deciliter for U.S. adults was 199 with a standard deviation of 44. A random sample of 104 adults was
Chosen. What is the probability that the mean cholesterol level is less than 198?

A) 0.4920
B) 0.5080
C) 0.5910
D) 0.4090

Question 70

The mean annual income for people in a certain city (in thousands of dollars) is 42, with a standard deviation of 30. A pollster draws a sample of 47 people to interview. Find the 84th percentile of the
Sample mean.

A) 49.0 thousand dollars
B) 43.6 thousand dollars
C) 44.0 thousand dollars
D) 46.3 thousand dollars

Question 71

A certain car model has a mean gas mileage of 34 miles per gallon (mpg) with a standard deviation 4 mpg. A pizza delivery company buys 54 of these cars. What is the probability that the average
Mileage of the fleet is between 33.3 and 34.3 mpg?

A) 0.6103
B) 0.0985
C) 0.7088
D) 0.3897

Question 72

Use technology to solve the following problem: A ferry will safely accommodate 79 tons of passenger cars. Assume that the mean weight of a passenger car is 1.9 tons with standard deviation
0)5 tons. If a random sample of 39 cars are loaded onto the ferry, what is the probability that the
Maximum safe weight will be exceeded?

A) 0.0516
B) 0.9417
C) 0.0583
D) 0.0669

Question 73

Use technology to solve the following problem: A certain car model has a mean gas mileage of 33 miles per gallon (mpg) with a standard deviation 3 mpg. A pizza delivery company buys 48 of these
Cars. What is the probability that the average mileage of the fleet is between 32.7 and 33.3 mpg?

A) 0.5116
B) 0.4884
C) 0.2442
D) 0.7558

Question 74

Use technology to solve the following problem: A sample of size 52 will be drawn from a population with mean 11 and standard deviation 11. Find the probability that will be greater than
13)

A) 0.1001
B) 0.0667
C) 0.0949
D) 0.9051

Question 75

The mean number of pets per household is 3.33 with standard deviation 1.6. A sample of 53 households is drawn. Find the 78th percentile of the sample mean.

A) 4.35
B) 3.50
C) 4.20
D) 2.89

Question 76

The mean annual income for people in a certain city (in thousands of dollars) is 39, with a standard deviation of 36. A pollster draws a sample of 43 people to interview. What is the probability that the
Sample mean income is less than 33 (thousands of dollars)?

A) 0.1379
B) 0.8186
C) 0.1814
D) 0.1151

Question 77

Use technology to solve the following problem: The mean annual income for people in a certain city (in thousands of dollars) is 45, with a standard deviation of 37. A pollster draws a sample of 37
People to interview. What is the probability that the sample mean income is less than 52 (thousands
Of dollars)?

A) 0.8751
B) 0.8391
C) 0.1019
D) 0.8981

Question 78

A ferry will safely accommodate 86 tons of passenger cars. Assume that the mean weight of a passenger car is 2.1 tons with standard deviation 0.6 tons. If a random sample of 38 cars are loaded
Onto the ferry, what is the probability that the maximum safe weight will be exceeded?

A) 0.0485
B) 0.9535
C) 0.0465
D) 0.0668

Question 79

Use technology to solve the following problem: The mean annual income for people in a certain city (in thousands of dollars) is 40, with a standard deviation of 38. A pollster draws a sample of 35
People to interview. Find the 50th percentile of the sample mean.

A) 37.1 thousand dollars
B) 43.1 thousand dollars
C) 38.2 thousand dollars
D) 40.0 thousand dollars

Question 80

Use technology to solve the following problem: The mean annual income for people in a certain city (in thousands of dollars) is 44, with a standard deviation of 35. A pollster draws a sample of 59
People to interview. What is the probability that the sample mean income is between 42 and
48 (thousands of dollars)?

A) 0.5204
B) 0.4796
C) 0.8100
D) 0.1900