   # Consider a sample with a mean of 30 and a standard deviation of 5. Use Chebyshev’s theorem to determine the percentage of the data within each of the following ranges: a. 20 to 40 b. 15 to 45 c. 22 to 38 d. 18 to 42 e. 12 to 48 13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

#### Solutions

Chapter
Section 13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
Chapter 3.3, Problem 37E
Textbook Problem
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## Consider a sample with a mean of 30 and a standard deviation of 5. Use Chebyshev’s theorem to determine the percentage of the data within each of the following ranges: a. 20 to 40 b. 15 to 45 c. 22 to 38 d. 18 to 42 e. 12 to 48

a.

To determine

Find the percentage of the data within the range 20 to 40 using Chebyshev’s theorem.

### Explanation of Solution

Calculation:

The given information is that the mean and standard deviation of the sample are 30 and 5, respectively.

The formula for z-score is zi=xix¯s.

Where x¯ is the sample mean and s is the sample standard deviation.

The z-score corresponding to 20 can be obtained as follows:

Substitute xi=20, s=30 and x¯=5

z=20305=2

Thus, the z-score corresponding to 20 is –2.

The z-score corresponding to 40 can be obtained as follows:

Substitute xi=40, s=30 and x¯

b.

To determine

Find the percentage of the data within the range 15 to 45, using Chebyshev’s theorem.

c.

To determine

Find the percentage of the data within the range 22 to 38, using Chebyshev’s theorem.

d.

To determine

Find the percentage of the data within the range 18 to 42, using Chebyshev’s theorem.

e.

To determine

Find the percentage of the data within the range 12 to 48, using Chebyshev’s theorem.

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