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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.

**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

Where

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

Substitute

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

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

Substitute

**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.

STATISTICS F/BUSINESS+ECONOMICS-TEXT

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