 # C J The local police force gives all applicants an entrance exam and accepts only those applicants who score in the top l5% on this test. If the mean score this year is 87 and the standard deviation is 8, would an individual with a score of 110 be accepted? ### 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 5.11P
Textbook Problem
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## C J The local police force gives all applicants an entrance exam and accepts only those applicants who score in the top l5% on this test. If the mean score this year is 87 and the standard deviation is 8, would an individual with a score of 110 be accepted?

Expert Solution
To determine

To find:

If an individual with a score of 110 is accepted in the local police force.

### Explanation of Solution

Given:

The local police force gives all applicants an entrance exam and accepts only those applicants who score in the top 15% on this test. The mean score is 87 and the standard deviation is 8.

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 87 and standard deviation is 8.

For the score of 110,

Substitute 110 for Xi, 87 for X¯, and 8 for s in the above mentioned formula,

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