Question

Step 1

*Chebyshev’s inequality:*

Chebyshev’s rule is appropriate for any distribution. That is, Chebyshev’s inequality applies to all distributions, regardless of shape. Moreover, it provides the minimum percentage of the observation that lies within *k* standard deviations of the mean.

- It is possible that very few measurements will fall within 1 standard deviation of the mean.
- If
*k*= 2, at least 3/4 of the measurements lie within 2 standard deviations to either side of the mean. - If
*k*= 3, at least 8/9 of the measurements lie within 3 standard deviations to either side of the mean. - Generally, for any number
*k*greater than 1, at least (1-1/k^{2}) of the measurements will fall within*k*standard deviations of the mean.

Step 2

It was found that the body temperatures of healthy adults have a bell shaped distribution with a mean of 98.07^{0}F and a standard deviation of 0.56^{0}F.

Using Chebyshev’s theorem, at least 8/9 of the measurements lie within 3 standard deviations to either side of the mean.

Thus, 88.9% of healthy adults have body temperatures are within 3 standard deviations of the mean.

That is, according to Chebyshev’s rule, at least 88.9% of the observations fall within the interval *x*-bar±3*s*.

Step 3

Thus, at least 88.9% (approximately 89%) of the healthy adults have body temperatures between 96.39 and 99.75.

Hence, the minimum an...

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