Question

The body temperatures of a group of healthy adults have a​ bell-shaped distribution with a mean of 98.39degreesF and a standard deviation of 0.48degreesF. 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 97.43degreesF and 99.35degrees​F? b. What is the approximate percentage of healthy adults with body temperatures between 97.91degreesF and 98.87degrees​F?

Answer 1

a) 95%

b) 68%

Step-by-step explanation:

Here the distribution given to us is:

`X \sim N(98.39, 0.48^2)`

a) 97.43 can be written as 98.39 - 2\times 0.48 that is 2 standard deviation.

According to empirical rule, 95% of the observations lies within 2 standard deviations of the mean.

Therefore 95% is the correct answer here.

b) 97.91 can be written as: 98.39 - 1*0.53 that is 1 standard deviations less than the mean

Also, 98.87 = 98.39 + 0.48 that is 1 standard deviations above the mean.

According to the empirical rule, 68% of the observations lies within 1 standard deviation of the mean.