 # The senior class has been given a comprehensive examination to assess educational experience. The mean score on the test was 74 and the standard deviation was 10. What percentage of the students had scores a. between 75 and 85? __________ b. between 80 and 85? ________ c. above 80? _____________ d. above 83? ____________ e. between 80 and 70? ____________ f. between 75 and 70? ___________ g. below 75? ___________ h. below 77? __________ i. below 80? _______ j. below 85? ____________ ### 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 5.3P
Textbook Problem
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## The senior class has been given a comprehensive examination to assess educational experience. The mean score on the test was 74 and the standard deviation was 10. What percentage of the students had scoresa. between 75 and 85? __________b. between 80 and 85? ________c. above 80? _____________d. above 83? ____________e. between 80 and 70? ____________f. between 75 and 70? ___________g. below 75? ___________h. below 77? __________i. below 80? _______j. below 85? ____________

Expert Solution
To determine

a)

To find:

The percentage of students between the scores of 75 and 85.

### Explanation of Solution

Given:

The mean score of the test is 74 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 74 and standard deviation is 10.

For the score of 75,

Substitute 75 for Xi, 74 for X¯, and 10 for s in the above mentioned formula,

Z=757410=110=0

Expert Solution
To determine

b)

To find:

The percentage of students between the scores of 80 and 85.

Expert Solution
To determine

c)

To find:

The percentage of students above the score of 80.

Expert Solution
To determine

d)

To find:

The percentage of students above the score of 83.

Expert Solution
To determine

e)

To find:

The percentage of students between the scores of 80 and 70.

Expert Solution
To determine

f)

To find:

The percentage of students between the scores of 75 and 70.

Expert Solution
To determine

g)

To find:

The percentage of students below the score of 75.

Expert Solution
To determine

h)

To find:

The percentage of students below the score of 77.

Expert Solution
To determine

i)

To find:

The percentage of students below the score of 80.

Expert Solution
To determine

j)

To find:

The percentage of students below the score of 85.

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