Deck 6: The Normal Distribution and Other Continuous Distributions

Question 1

The value of the cumulative standardized normal distribution at 1.5X is 0.9332. The value of X is

A) 0.10
B) 0.50
C) 1.00
D) 1.50

Answer 1

C

Question 2

The owner of a fish market determined that the mean weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound. A citation catfish should be one of the top 2% in weight.
Assuming the weights of catfish are normally distributed, at what weight (in pounds) should the
Citation designation be established?

A) 1.56 pounds
B) 4.84 pounds
C) 5.20 pounds
D) 7.36 pounds

Answer 2

B

Question 3

A company that sells annuities must base the annual payout on the probability distribution of the
length of life of the participants in the plan. Suppose the probability distribution of the lifetimes
of the participants is approximately a normal distribution with a mean of 68 years and a standard
deviation of 3.5 years. What proportion of the plan recipients die before they reach the standard
retirement age of 65?

Answer 3

0.1957 using Excel or 0.1949 using Table E.2

Question 4

If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1
Minute, find the probability that a randomly selected college student will take between 2 and 4.5
Minutes to find a parking spot in the library parking lot.

A) 0.0919
B) 0.2255
C) 0.4938
D) 0.7745

Question 5

Given that X is a normally distributed variable with a mean of 50 and a standard deviation of 2,
find the probability that X is between 47 and 54.

Question 6

The owner of a fish market determined that the mean weight for a catfish is 3.2 pounds with a
standard deviation of 0.8 pound. Assuming the weights of catfish are normally distributed, the
probability that a randomly selected catfish will weigh less than 2.2 pounds is _______?

Question 7

In its standardized form, the normal distribution

A) has a mean of 0 and a standard deviation of 1.
B) has a mean of 1 and a variance of 0.
C) has an area equal to 0.5.
D) cannot be used to approximate discrete probability distributions.

Question 8

Which of the following about the normal distribution is not true?

A) Theoretically, the mean, median, and mode are the same.
B) About 2/3 of the observations fall within ± 1 standard deviation from the mean.
C) It is a discrete probability distribution.
D) Its parameters are the mean, μ, and standard deviation, σ.

Question 9

A company that sells annuities must base the annual payout on the probability distribution of the
length of life of the participants in the plan. Suppose the probability distribution of the lifetimes
of the participants is approximately a normal distribution with a mean of 68 years and a standard
deviation of 3.5 years. Find the age at which payments have ceased for approximately 86% of the
plan participants.

Question 10

For some value of Z, the value of the cumulative standardized normal distribution is 0.2090. The value of Z is

A) - 0.81
B) - 0.31
C) 0.31
D) 1.96

Question 11

For some value of Z, the value of the cumulative standardized normal distribution is 0.8340. The value of Z is

A) 0.07
B) 0.37
C) 0.97
D) 1.06

Question 12

The value of the cumulative standardized normal distribution at Z is 0.8770. The value of Z is

A) 0.18
B) 0.81
C) 1.16
D) 1.47

Question 13

A company that sells annuities must base the annual payout on the probability distribution of the
length of life of the participants in the plan. Suppose the probability distribution of the lifetimes
of the participants is approximately a normal distribution with a mean of 68 years and a standard
deviation of 3.5 years. What proportion of the plan recipients would receive payments beyond
age 75?

Question 14

If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1
Minute, find the probability that a randomly selected college student will find a parking spot in
The library parking lot in less than 3 minutes.

A) 0.3551
B) 0.3085
C) 0.2674
D) 0.1915

Question 15

The owner of a fish market determined that the mean weight for a catfish is 3.2 pounds with a
standard deviation of 0.8 pound. Assuming the weights of catfish are normally distributed, above
what weight (in pounds) do 89.80% of the weights occur?

Question 16

If a particular set of data is approximately normally distributed, we would find that approximately

A) 2 of every 3 observations would fall between ± 1 standard deviation around the mean.
B) 4 of every 5 observations would fall between ± 1.28 standard deviations around the mean.
C) 19 of every 20 observations would fall between ± 2 standard deviations around the mean.
D) All the above.

Question 17

The value of the cumulative standardized normal distribution at Z is 0.6255. The value of Z is

A) 0.99
B) 0.40
C) 0.32
D) 0.16

Question 18

The owner of a fish market determined that the mean weight for a catfish is 3.2 pounds with a
standard deviation of 0.8 pound. Assuming the weights of catfish are normally distributed, the
probability that a randomly selected catfish will weigh more than 4.4 pounds is _______?

Question 19

The owner of a fish market determined that the mean weight for a catfish is 3.2 pounds with a
standard deviation of 0.8 pound. Assuming the weights of catfish are normally distributed, the
probability that a randomly selected catfish will weigh between 3 and 5 pounds is _______?

Question 20

If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1
Minute, 75.8% of the college students will take more than how many minutes when trying to find
A parking spot in the library parking lot?

A) 2.8 minutes
B) 3.2 minutes
C) 3.4 minutes
D) 4.2 minutes

Question 21

Any set of normally distributed data can be transformed to its standardized form.

Question 22

The true length of boards cut at a mill with a listed length of 10 feet is normally distributed with a
mean of 123 inches and a standard deviation of 1 inch. What proportion of the boards will be
between 121 and 124 inches?

Question 23

The true length of boards cut at a mill with a listed length of 10 feet is normally distributed with a
mean of 123 inches and a standard deviation of 1 inch. What proportion of the boards will be less
than 124 inches?

Question 24

A food processor packages orange juice in small jars. The weights of the filled jars are
approximately normally distributed with a mean of 10.5 ounces and a standard deviation of 0.3
ounce. Find the proportion of all jars packaged by this process that have weights that fall above
10.95 ounces.

Question 25

Theoretically, the mean, median, and the mode are all equal for a normal
distribution.

Question 26

The "middle spread," that is the middle 50% of the normal distribution, is equal to
one standard deviation.

Question 27

The probability that a standard normal variable, Z, falls between -2.00 and -0.44
is 0.6472.

Question 28

A normal probability plot may be used to assess the assumption of normality for a
particular set of data.

Question 29

You were told that the amount of time lapsed between consecutive trades on a foreign stock
exchange market followed a normal distribution with a mean of 15 seconds. You were also told
that the probability that the time lapsed between two consecutive trades to fall between 16 to 17
seconds was 13%. The probability that the time lapsed between two consecutive trades would
fall below 13 seconds was 7%. What is the probability that the time lapsed between two
consecutive trades will be longer than 17 seconds?

Question 30

The probability that a standard normal variable, Z, is less than 5.0 is
approximately 0.

Question 31

You were told that the amount of time lapsed between consecutive trades on a foreign stock
exchange market followed a normal distribution with a mean of 15 seconds. You were also told
that the probability that the time lapsed between two consecutive trades to fall between 16 to 17
seconds was 13%. The probability that the time lapsed between two consecutive trades would fall
below 13 seconds was 7%. What is the probability that the time lapsed between two consecutive
trades will be between 13 and 14 seconds?

Question 32

The true length of boards cut at a mill with a listed length of 10 feet is normally distributed with a
mean of 123 inches and a standard deviation of 1 inch. What proportion of the boards will be over
125 inches in length?

Question 33

A food processor packages orange juice in small jars. The weights of the filled jars are
approximately normally distributed with a mean of 10.5 ounces and a standard deviation of 0.3
ounce. Find the proportion of all jars packaged by this process that have weights that fall below
10.875 ounces.

Question 34

If a data set is approximately normally distributed, its normal probability plot
would be S-shaped.

Question 35

The probability that a standard normal variable, Z, is between 1.50 and 2.10 is the
same as the probability Z is between - 2.10 and - 1.50.

Question 36

The probability that a standard normal variable Z is positive is ________.

Question 37

The probability that a standard normal variable, Z, is between 1.00 and 3.00 is
0.1574.

Question 38

The probability that a standard normal variable, Z, falls between - 1.50 and 0.81 is
0.7242.

Question 39

A worker earns $15 per hour at a plant in China and is told that only 2.5% of all
workers make a higher wage. If the wage is assumed to be normally distributed and the standard
deviation of wage rates is $5 per hour, the mean wage for the plant is $7.50 per hour.

Question 40

The probability that a standard normal variable, Z, is below 1.96 is 0.4750.

Question 41

You were told that the mean score on a statistics exam is 75 with the scores normally distributed.
In addition, you know the probability of a score between 55 and 60 is 4.41% and that the
probability of a score greater than 90 is 6.68%. What is the probability of a score between 90 and
95?

Question 42

You were told that the mean score on a statistics exam is 75 with the scores normally distributed.
In addition, you know the probability of a score between 55 and 60 is 4.41% and that the
probability of a score greater than 90 is 6.68%. What is the probability of a score between 60 and
75?

Question 43

You were told that the mean score on a statistics exam is 75 with the scores normally distributed.
In addition, you know the probability of a score between 55 and 60 is 4.41% and that the
probability of a score greater than 90 is 6.68%. What is the probability of a score between 55 and
95?

Question 44

You were told that the amount of time lapsed between consecutive trades on a foreign stock
exchange market followed a normal distribution with a mean of 15 seconds. You were also told
that the probability that the time lapsed between two consecutive trades to fall between 16 to 17
seconds was 13%. The probability that the time lapsed between two consecutive trades would fall
below 13 seconds was 7%. What is the probability that the time lapsed between two consecutive
trades will be between 14 and 15 seconds?

Question 45

You were told that the mean score on a statistics exam is 75 with the scores normally distributed.
In addition, you know the probability of a score between 55 and 60 is 4.41% and that the
probability of a score greater than 90 is 6.68%. What is the probability of a score greater than
95?

Question 46

You were told that the mean score on a statistics exam is 75 with the scores normally distributed.
In addition, you know the probability of a score between 55 and 60 is 4.41% and that the
probability of a score greater than 90 is 6.68%. What is the probability of a score between 60 and
95?

Question 47

You were told that the amount of time lapsed between consecutive trades on a foreign stock
exchange market followed a normal distribution with a mean of 15 seconds. You were also told
that the probability that the time lapsed between two consecutive trades to fall between 16 to 17
seconds was 13%. The probability that the time lapsed between two consecutive trades would fall
below 13 seconds was 7%. What is the probability that the time lapsed between two consecutive
trades will be between 13 and 16 seconds?

Question 48

You were told that the amount of time lapsed between consecutive trades on a foreign stock
exchange market followed a normal distribution with a mean of 15 seconds. You were also told
that the probability that the time lapsed between two consecutive trades to fall between 16 to 17
seconds was 13%. The probability that the time lapsed between two consecutive trades would fall
below 13 seconds was 7%. What is the probability that the time lapsed between two consecutive
trades will be between 14 and 17 seconds?

Question 49

You were told that the mean score on a statistics exam is 75 with the scores normally distributed.
In addition, you know the probability of a score between 55 and 60 is 4.41% and that the
probability of a score greater than 90 is 6.68%. The middle 95.46% of the students will score
between which two scores?

Question 50

You were told that the mean score on a statistics exam is 75 with the scores normally distributed.
In addition, you know the probability of a score between 55 and 60 is 4.41% and that the
probability of a score greater than 90 is 6.68%. What is the probability of a score lower than 55?

Question 51

You were told that the amount of time lapsed between consecutive trades on a foreign stock
exchange market followed a normal distribution with a mean of 15 seconds. You were also told
that the probability that the time lapsed between two consecutive trades to fall between 16 to 17
seconds was 13%. The probability that the time lapsed between two consecutive trades would fall
below 13 seconds was 7%. What is the probability that the time lapsed between two consecutive
trades will be between 15 and 16 seconds?

Question 52

You were told that the mean score on a statistics exam is 75 with the scores normally distributed.
In addition, you know the probability of a score between 55 and 60 is 4.41% and that the
probability of a score greater than 90 is 6.68%. What is the probability of a score between 55 and
90?

Question 53

You were told that the mean score on a statistics exam is 75 with the scores normally distributed.
In addition, you know the probability of a score between 55 and 60 is 4.41% and that the
probability of a score greater than 90 is 6.68%. What is the probability of a score between 75 and
90?

Question 54

You were told that the amount of time lapsed between consecutive trades on a foreign stock
exchange market followed a normal distribution with a mean of 15 seconds. You were also told
that the probability that the time lapsed between two consecutive trades to fall between 16 to 17
seconds was 13%. The probability that the time lapsed between two consecutive trades would fall
below 13 seconds was 7%. The probability is 80% that the time lapsed will be longer than how
many seconds?

Question 55

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The
probability that Z is more than 0.77 is __________.

Question 56

You were told that the amount of time lapsed between consecutive trades on a foreign stock
exchange market followed a normal distribution with a mean of 15 seconds. You were also told
that the probability that the time lapsed between two consecutive trades to fall between 16 to 17
seconds was 13%. The probability that the time lapsed between two consecutive trades would fall
below 13 seconds was 7%. The middle 86% of the time lapsed will fall between which two
numbers?

Question 57

You were told that the amount of time lapsed between consecutive trades on a foreign stock
exchange market followed a normal distribution with a mean of 15 seconds. You were also told
that the probability that the time lapsed between two consecutive trades to fall between 16 to 17
seconds was 13%. The probability that the time lapsed between two consecutive trades would fall
below 13 seconds was 7%. The probability is 20% that the time lapsed will be shorter how many
seconds?

Question 58

You were told that the amount of time lapsed between consecutive trades on a foreign stock
exchange market followed a normal distribution with a mean of 15 seconds. You were also told
that the probability that the time lapsed between two consecutive trades to fall between 16 to 17
seconds was 13%. The probability that the time lapsed between two consecutive trades would fall
below 13 seconds was 7%. The middle 60% of the time lapsed will fall between which two
numbers?

Question 59

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The
probability that Z is less than 1.15 is __________.

Question 60

You were told that the mean score on a statistics exam is 75 with the scores normally distributed.
In addition, you know the probability of a score between 55 and 60 is 4.41% and that the
probability of a score greater than 90 is 6.68%. The middle 86.64% of the students will score
between which two scores?

Question 61

The amount of time necessary for assembly line workers to complete a product is a normal
variable with a mean of 15 minutes and a standard deviation of 2 minutes. The probability is
__________ that a product is assembled in between 14 and 16 minutes.

Question 62

The amount of time necessary for assembly line workers to complete a product is a normal
variable with a mean of 15 minutes and a standard deviation of 2 minutes. The probability is
__________ that a product is assembled in more than 19 minutes.

Question 63

The amount of time necessary for assembly line workers to complete a product is a normal
variable with a mean of 15 minutes and a standard deviation of 2 minutes. The probability is
__________ that a product is assembled in more than 11 minutes.

Question 64

The amount of time necessary for assembly line workers to complete a product is a normal
variable with a mean of 15 minutes and a standard deviation of 2 minutes. The probability is
__________ that a product is assembled in between 16 and 21 minutes.

Question 65

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The
probability that Z is between -2.89 and -1.03 is __________.

Question 66

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. So
96% of the possible Z values are between __________ and __________ (symmetrically
distributed about the mean).

Question 67

The amount of time necessary for assembly line workers to complete a product is a normal
variable with a mean of 15 minutes and a standard deviation of 2 minutes. The probability is
__________ that a product is assembled in between 15 and 21 minutes.

Question 68

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The
probability that Z is between -0.88 and 2.29 is __________.

Question 69

The amount of time necessary for assembly line workers to complete a product is a normal
variable with a mean of 15 minutes and a standard deviation of 2 minutes. The probability is
__________ that a product is assembled in less than 20 minutes.

Question 70

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The
probability that Z is less than -2.20 is __________.

Question 71

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The
probability that Z values are larger than __________ is 0.6985.

Question 72

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The
probability that Z is between -2.33 and 2.33 is __________.

Question 73

The amount of time necessary for assembly line workers to complete a product is a normal
variable with a mean of 15 minutes and a standard deviation of 2 minutes. The probability is
__________ that a product is assembled in less than 12 minutes.

Question 74

The amount of time necessary for assembly line workers to complete a product is a normal
variable with a mean of 15 minutes and a standard deviation of 2 minutes. So, 15% of the
products require more than __________ minutes for assembly.

Question 75

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. So
50% of the possible Z values are between __________ and __________ (symmetrically
distributed about the mean).

Question 76

The amount of time necessary for assembly line workers to complete a product is a normal
variable with a mean of 15 minutes and a standard deviation of 2 minutes. The probability is
__________ that a product is assembled in between 10 and 12 minutes.

Question 77

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The
probability that Z is more than -0.98 is __________.

Question 78

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. So
27% of the possible Z values are smaller than __________.

Question 79

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The
probability that Z values are larger than __________ is 0.3483.

Question 80

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. So
85% of the possible Z values are smaller than __________.