 # For a normal distribution where the mean is 50 and the standard deviation is 10, what percentage of the area is a. between the scores of 40 and 47? __________ b. above a score of 47? ________ c. below a score of 53? _____________ d. between the scores of 35 and 65? ____________ e. above a score of 72? ____________ f. below a score of 31 and above a score of 69? ___________ g. between the scores of 55 and 62? ___________ h. between the scores of 32 and 47? __________ ### Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836 ### Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836

#### Solutions

Chapter
Section
Chapter 5, Problem 5.4P
Textbook Problem
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## For a normal distribution where the mean is 50 and the standard deviation is 10, what percentage of the area isa. between the scores of 40 and 47? __________b. above a score of 47? ________c. below a score of 53? _____________d. between the scores of 35 and 65? ____________e. above a score of 72? ____________f. below a score of 31 and above a score of 69? ___________g. between the scores of 55 and 62? ___________h. between the scores of 32 and 47? __________

Expert Solution
To determine

a)

To find:

The percentage of students between the scores of 40 and 47.

### Explanation of Solution

Given:

The mean score of the test is 50 and the standard deviation is 10.

Description:

The normal curve is symmetrical and its mean is equal to the median. The area below and above the mean is 50% or 0.05.

Formula used:

Let the data values be denoted by Xi.

The formula to calculate the Z score is given by,

Z=XiX¯s

Where, X¯ is the mean and s is the standard deviation of the distribution.

Calculation:

Given that the mean is 50 and standard deviation is 10.

For the score of 40,

Substitute 40 for Xi, 50 for X¯, and 10 for s in the above mentioned formula,

Z=405010=1010=1

The area between the mean and the score 1 is 0

Expert Solution
To determine

b)

To find:

The percentage of students above the scores of 47.

Expert Solution
To determine

c)

To find:

The percentage of students below the score of 53.

Expert Solution
To determine

d)

To find:

The percentage of students between the scores of 35 and 65.

Expert Solution
To determine

e)

To find:

The percentage of students above the scores of 72.

Expert Solution
To determine

f)

To find:

The percentage of students below a score of 31 and above a score of 69.

Expert Solution
To determine

g)

To find:

The percentage of students between the scores of 55 and 62.

Expert Solution
To determine

h)

To find:

The percentage of students between the scores of 32 and 47.

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