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Chebyshev鈥檚Theorem Based on Data Set 3 鈥淏ody Temperatures鈥 in Appendix B, body temperatures of healthy adults have a bell-shaped distribution with a mean of 98.20掳F and a standard deviation of 0.62掳F (using the data from 12 AM on day 2). Using Chebyshev鈥檚 theorem, what do we know about the percentage of healthy adults with body temperatures that are within 2 standard deviations of the mean? What are the minimum and maximum body temperatures that are within 2 standard deviations of the mean??

Short Answer

Expert verified

75% of adults have a body temperature within two standard deviations of the mean.

The maximum body temperature that falls within two standard deviations of the mean is equal to 99.44 Fo, and the minimum body temperature that falls within two standard deviations of the mean is equal to 96.96 Fo.

Step by step solution

01

Given information

The body temperatures of adults are provided in degrees Fahrenheit.

The mean body temperature is equal to 98.20Fo, and the standard deviation of the body temperature is equal to 0.62 Fo.

02

Chebyshev’s theorem

For a dataset that approximately follows the bell-shaped probability distribution, Chebyshev鈥檚 theorem can be applied. The theorem states that at least 1-1K2values lie between K standard deviations of the mean.

Here, K=2

1-1K2=1-122=1-14=34

Hence, 34or approximately 75%of healthy adults have a body temperature within two standard deviations of the mean.

According to the given value of K, the limits come out to be equal to:

-2=98.20-20.62=96.96+2=98.20+20.62=99.44

Therefore, the maximum value of body temperature between these limits is equal to 99.44 Fo, and the minimum valueof body temperature between these limits is equal to 96.96 Fo.

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