Statistics: Concepts and Controversies
Statistics: Concepts and Controversies
9th Edition
ISBN: 9781464192937
Author: David S. Moore, William I. Notz
Publisher: W. H. Freeman
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Chapter 13, Problem 1CS

Section 1

To determine

To find: The temperatures between which the 68% of body temperatures fall.

Section 1

Expert Solution
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Answer to Problem 1CS

Solution: The 68% of body temperatures fall between 97.52F and 98.98F.

Explanation of Solution

Given: The distribution of body temperatures is normal and the mean and standard deviation of the distribution are 98.25F and 0.73F, respectively.

Calculation:

The 689599.7 rule states that 68% of the data that has normal distribution falls within one standard deviation of the mean. The one standard deviation of the mean is defined as (μσ) and (μ+σ).

With the provided values of mean and standard deviation, the range of body temperatures can be obtained in which 68% values of the body temperatures will fall.

The range of the body temperatures will be calculated as

μσ=98.25(1×0.73)=98.250.73=97.52

and

μ+σ=98.25+(1×0.73)=98.25+0.73=98.98

Therefore, the 68% of body temperatures will fall between 97.52F and 98.98F.

Section 2

To determine

To find: The temperatures between which the 95% of body temperatures fall.

Section 2

Expert Solution
Check Mark

Answer to Problem 1CS

Solution: The 95% of body temperatures fall between 96.79F and 99.71F.

Explanation of Solution

Calculation:

The 689599.7 rule states that middle 95% of the data that has normal distribution falls within two standard deviations of the mean. The two standard deviations of the mean are defined as (μ2σ) and (μ+2σ).

With the given values of mean and standard deviation, the range of body temperatures can be obtained in which 95% value of the body temperatures will fall.

The range of the body temperatures will be calculated as

μ2σ=98.25(2×0.73)=98.251.46=96.79

and

μ+2σ=98.25+(2×0.73)=98.25+1.46=99.71

Therefore, the 95% of body temperatures fall between 96.79F and 99.71F.

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