AnswersCommon Core Algebra II - MA3111 B-ICApplications with Standard Normal Distribution

Applications with Standard Normal Distribution Answers

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1
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A normal distribution of data has a mean of 15 and a standard deviation of 4. How many standard deviations from the mean is 25?

A
0.16
B
0.4
C
2.5
D
6.25
2
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What is the approximate area of the unshaded region under the standard normal curve below? Use the portion of the standard normal table given to help answer the question. z Probability0.000.50001.000.84132.000.97723.000.9987

Question illustration
A
0.02
B
0.16
C
0.18
D
0.82
3

For a standard normal distribution, find the approximate value of . Use the portion of the standard normal table below to help answer the question.zProbability0.000.50000.250.59871.000.84131.250.89441.500.93321.750.9599

Question illustration
A
11%
B
39%
C
61%
D
89%
4

The times of the runners in a marathon are normally distributed, with a mean of 3 hours and 50 minutes and a standard deviation of 30 minutes. What is the probability that a randomly selected runner has a time less than or equal to 3 hours and 20 minutes? Use the portion of the standard normal table below to help answer the question.zProbability0.000.50000.500.69151.000.84132.000.97723.000.9987

A
16%
B
32%
C
34%
D
84%
5

About what percentage of the data lies within 2 standard deviations of the mean in a normal distribution?

A
47.5%
B
68%
C
95%
D
99.7%
6

For a standard normal distribution, find the approximate value of . Use the portion of the standard normal table below to help answer the question.zProbability0.000.50000.220.58710.320.62550.420.66280.440.67000.640.73890.840.79951.000.8413

Question illustration
A
16%
B
34%
C
66%
D
84%
8

For a standard normal distribution, which of the following variables always equals 0?

A
Mu
Option A
B
Sigma
Option B
C
x
D
z
9

The times of the runners in a marathon are normally distributed, with a mean of 3 hours and 50 minutes and a standard deviation of 30 minutes. What is the probability that a randomly selected runner has a time less than or equal to 3 hours and 20 minutes? Use the portion of the standard normal table below to help answer the question.zProbability0.000.50000.500.69151.000.84132.000.97723.000.9987

A
16%
B
32%
C
34%
D
84%
10

Which of the following probabilities is equal to approximately 0.2957? Use the portion of the standard normal table below to help answer the question.zProbability0.000.50000.250.59870.500.69150.750.77341.000.84131.250.89441.500.93321.750.9599

A
P (negative 1.25 less-than-or-equal-to z less-than-or-equal-to 0.25)
Option A
B
P (negative 1.25 less-than-or-equal-to z less-than-or-equal-to 0.75)
Option B
C
P (0.25 less-than-or-equal-to z less-than-or-equal-to 1.25)
Option C
D
P (0.75 less-than-or-equal-to z less-than-or-equal-to 1.25)
Option D
11

A normal distribution of data has a mean of 15 and a standard deviation of 4. How many standard deviations from the mean is 25?

A
0.16
B
0.4
C
2.5
D
6.25
12

About what percentage of the data lies within 2 standard deviations of the mean in a normal distribution?

A
47.5%
B
68%
C
95%
D
99.7%
13

What is the approximate area of the unshaded region under the standard normal curve below? Use the portion of the standard normal table given to help answer the question. z Probability0.000.50001.000.84132.000.97723.000.9987

Question illustration
A
0.02
B
0.16
C
0.18
D
0.82
14

If a data value in a normal distribution has a negative z-score, which of the following must be true?

A
The data value must be negative.
B
The data value must be positive.
C
The data value must be less than the mean.
D
The data value must be greater than the mean.
15

For a standard normal distribution, find the approximate value of . Use the portion of the standard normal table below to help answer the question.zProbability0.000.50000.250.59871.000.84131.250.89441.500.93321.750.9599

Question illustration
A
11%
B
39%
C
61%
D
89%
16

What is the approximate area of the shaded region under the standard normal curve below? Use the portion of the standard normal table to help answer the question.zProbability0.000.50001.000.84132.000.97723.000.9987

Question illustration
A
0.16
B
0.68
C
0.82
D
0.84
17

What is the approximate area of the unshaded region under the standard normal curve below? Use the portion of the standard normal table given to help answer the question. z Probability0.000.50001.000.84132.000.97723.000.9987

Question illustration
A
0.14
B
0.16
C
0.86
D
0.98
18

The probability that a random variable is greater than or equal to z standard deviations from the mean in a standard normal distribution is p%. What can be said with certainty about the probability that the random variable is less than or equal to –z standard deviations from the mean?

A
The probability is less than p%.
B
The probability is equal to p%.
C
The probability is greater than p%.
D
The probability is not equal to p%.
19

For a standard normal distribution, if , what is the value of ?

Question illustration
A
0.2116
B
0.2884
C
0.7116
D
0.7884

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