Answer to Question #143517 in Statistics and Probability for Vladimyr Lubin

Question

The body temperatures of a group of healthy adults have a​ bell-shaped distribution with a mean of 98.11F and a standard deviation of 0.56F. Using the empirical​ rule, find each approximate percentage below.
a.What is the approximate percentage of healthy adults with body temperatures within standard of the​ mean, or between 97.55F and 98.67F?
b.What is the approximate percentage of healthy adults with body temperatures between 96.43F and ​99.79F?
Approximately ? ​% of healthy adults in this group have body temperatures within 1 standard of the​ mean, or between 97.55F and 98.67F.

Answer 1

mean = 98.11F

standard deviation = 0.56F

a) 98.67 – 98.11 = 0.56 = 1 standard deviation

97.55 – 98.11 = –0.56 = 1 standard deviation

So 97.55F and 98.67F are 1 standard deviation from the mean 98.11F.

By the empirical rule we know that 68% of the data lies within 1 standard deviation of the mean.

b) 99.79 – 98.11 = 1.68 = 3 standard deviations

96.43 – 98.11 = –1.68 = –3 standard deviations

96.43F and ​99.79F are 3 standard deviations from the mean 98.11F.

By the empirical rule we know that 99.7% of the data lies within 3 standard deviation of the mean.

Approximately 68% of healthy adults in this group have body temperatures within 1 standard of the​ mean, or between 97.55F and 98.67F.