Answer to Question #234249 in Statistics and Probability for Yolie

Question

What is the approximate percentage of healthy adults with body temperatures between 97.12° And 99.32

Answer 1

QUESTION

The body temperatures of a group of healthy adults have a​ bell-shaped distribution with a mean of 98.37⁰F and a standard deviation of 0.49⁰F. Using the empirical​ rule, find each approximate percentage below.

a) What is the approximate percentage of healthy adults with body temperatures within 2 standard deviations of the​ mean, or between 97.39⁰F and 99.35⁰​F?

b) What is the approximate percentage of healthy adults with body temperatures between 97.88⁰F and 98.86⁰​F?

SOLUTION

Step-by-step explanation:

Mean = 98.37

Standard deviation = 0.49

Empirical rule

1 ) 68% of the information lies within 1 standard deviation of mean

like 68% of information lies between:  $\mu$ - $\sigma$ to $\mu$ + $\sigma$

So, On the available information

 98.37 - 0.49 to 98.37 + 0.49

 97.88 to 98.86

So, 68% of information lies between 97.88⁰F to 98.86⁰F.

2) 95% of the information lies within 2 standard deviation of mean

like 95% of information lies between:   $\mu$ - 2$\sigma$  to   $\mu$ - 2$\sigma$

So, On the available information

98.37 - 2(0.49) to 98.37 + 2(0.49)

97.39 to 99.35

So, 95% of information lies between 97.39⁰F to 99.35⁰F .

3) 99.7% of the information lies within 3 standard deviation of mean

like 99.7% of information lies between: $\mu$ - 3$\sigma$ to  $\mu$ - 3$\sigma$

So, On the available information

98.37 - 3(0.49) to 98.37 + 3(0.49)

96.90 to 99.84

So, 99.7% of information lies between 96.9°F to 99.84°F .

The approximate percentage of healthy adults with body temperatures within 2 standard deviations of the​ mean, or between 97.39°F to 99.35°F is 95%.

The approximate percentage of healthy adults with body temperatures between 97.88°F to 98.86°F is 68%.