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StatisticsEssentials Of StatisticsFor 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? __________BuyFind*arrow_forward*

4th Edition

HEALEY + 1 other

Publisher: Cengage Learning,

ISBN: 9781305093836

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 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? __________

Expert Solution

To determine

a)

**To find:**

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

**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

The formula to calculate the

Where,

**Calculation:**

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

For the score of 40,

Substitute 40 for

The area between the mean and the score

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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