Question

the body temperatures of a group of healthy adults have a bell - shaped distribution with a mean of (98.21^{circ}f) and a standard deviation of (0.65^{circ}f). using the empirical rule, find each approximate percentage below.
a. what is the approximate percentage of healthy adults with body temperatures within 1 standard deviation of the mean, or between (97.56^{circ}f) and (98.86^{circ}f)?
b. what is the approximate percentage of healthy adults with body temperatures between (96.26^{circ}f) and (100.16^{circ}f)?
a. approximately (square%) of healthy adults in this group have body temperatures within 1 standard deviation of the mean, or between (97.56^{circ}f) and (98.86^{circ}f).
(type an integer or a decimal. do not round.)

Explanation:

Step1: Recall the empirical rule

The empirical rule for a bell - shaped (normal) distribution states that approximately 68% of the data lies within 1 standard deviation of the mean, approximately 95% of the data lies within 2 standard deviations of the mean, and approximately 99.7% of the data lies within 3 standard deviations of the mean.

Step2: Calculate the number of standard deviations for part a

The mean is \(\mu = 98.21^{\circ}F\) and the standard deviation is \(\sigma=0.65^{\circ}F\).
For the lower bound: \(98.21 - 0.65=97.56^{\circ}F\)
For the upper bound: \(98.21 + 0.65 = 98.86^{\circ}F\)
Since these bounds are 1 standard deviation (\(z=\pm1\)) from the mean, by the empirical rule.

Answer:

68