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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Explain how to use the standard normal table to find the probability associated with the shaded area under the curve.

Answer:

Use the standard normal table to find the areas to the left of z = 1.9 and z = 0.4, then subtract the smaller left-tail area from the larger: 0.9713 - 0.6554 = 0.3159.

2
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%

Answer:

8

3

16%26%73%98%

A
16%
B
26%
C
73%
D
98%
4

Did your answer include the following?

A
The standard normal table gives areas under the curve to the left of z-scores.
B
Find the probability in the standard normal table that a value is to the left of 1.9.
C
Find the probability in the standard normal table that a value is to the left of 0.4.
D
Subtract the probability of a value being to the left of 0.4 from the probability of a value being to the left of 1.9.
5

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B
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6

1.251.52.5

A
1.25
B
1.5
C
2.5
7

P(z > –2.1)1–P(z 2.1)

A
P(z > –2.1)
B
1–P(z < 2.1)
C
P(z < 2.1)
D
1–P(z > 2.1)
8

Which statement represents the percent of American adults with total cholesterol scores in the borderline-high range?

A
Option
B
Option
C
Option
D
Option
9

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10

The life of a certain brand of battery is normally distributed, with mean 128 hours and standard deviation 16 hours. What is the probability that a battery you buy lasts at most 100 hours? Standardize the variable.x = 100 is equivalent to z = –0.570.57–1.751.75.

A
–0.57
B
0.57
C
–1.75
D
1.75
11

The probability that a battery you buy lasts at most 100 hours is about 4%16%84%96%.

A
4%
B
16%
C
84%
D
96%
12

Explain how to use the standard normal table to find the probability associated with the shaded area under the curve.

Question illustration
Answer:

To find the probability of the shaded area between z 0.4 and z 1.9, first use the standard normal table to find the cumulative area to the left of z 1.9. Then, find the cumulative area to the left of z 0.4. Subtract the area for z 0.4 from the area for z 1.9 to find the probability of being within that specific interval.

13

mc002-1.jpg

Question illustration
A
mc002-1.jpg
Option A
B
mc002-2.jpg
Option B
C
mc002-3.jpg
Option C
14

1.251.52.5

A
1.25
B
1.5
C
2.5
15

P(z > –2.1)1–P(z 2.1)

A
P(z > –2.1)
B
1–P(z < 2.1)
C
P(z < 2.1)
D
1–P(z > 2.1)
16

Which statement represents the percent of American adults with total cholesterol scores in the borderline-high range?

A
mc001-1.jpg
Option A
B
mc001-2.jpg
Option B
C
mc001-3.jpg
Option C
D
mc001-4.jpg
Option D
17

The life of a certain brand of battery is normally distributed, with mean 128 hours and standard deviation 16 hours. What is the probability that a battery you buy lasts at most 100 hours? Standardize the variable.x = 100 is equivalent to z = .

A
–0.57
B
0.57
C
–1.75
D
1.75
18

11%40%60%89%

A
11%
B
40%
C
60%
D
89%
19

0.01790.58320.98211

A
0.0179
B
0.5832
C
0.9821
D
1
20

Using the standard normal table, about what percent of American adults have borderline-high cholesterol levels?5%35%40%90%

A
5%
B
35%
C
40%
D
90%

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Applications with Standard Normal Distribution