 # For a math test on which the mean score was 59 and the standard deviation was 4, what is the probability that a student randomly selected from this class will have a score a. between 55 and 65? __________ b. between 60 and 65? ________ c. above 65? _____________ d. between 60 and 50? ____________ e. between 55 and 50? ___________ f. below 55? ___________ ### 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 5.9P
Textbook Problem
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## For a math test on which the mean score was 59 and the standard deviation was 4, what is the probability that a student randomly selected from this class will have a scorea. between 55 and 65? __________b. between 60 and 65? ________c. above 65? _____________d. between 60 and 50? ____________e. between 55 and 50? ___________f. below 55? ___________

Expert Solution
To determine

a)

To find:

The probability that the student selected will have a score between 55 and 65.

### Explanation of Solution

Given:

The distribution of the scores is normal with a mean of 59 and standard deviation of 4.

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 59 and standard deviation is 4.

For the score of 55,

Substitute 55 for Xi, 59 for X¯, and 4 for s in the above mentioned formula,

Z=55594=44=1

The area between mean and the score 1 is 0

Expert Solution
To determine

To find:

The probability that the student selected will have a score between 60 and 65.

Expert Solution
To determine

c)

To find:

The probability that the student selected will have a score above 65.

Expert Solution
To determine

d)

To find:

The probability that the student selected will have a score between 60 and 50.

Expert Solution
To determine

e)

To find:

The probability that the student selected will have a score between 55 and 50.

Expert Solution
To determine

To find:

The probability that the student selected will have a score below 55.

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