The Empirical Rule Based on Data Set 3 in Appendix B, body temperatures of healthy adults have a bell-shaped distribution with a mean of 98.20 ° F and a standard deviation of 0.62 ° F . Using the empirical rule, what is the approximate percentage of healthy adults with body temperatures

a. within 1 standard deviation of the mean, or between 97.58 ° F and 98.82 ° F ?

b. between 96.34 ° F and 100.06 ° F ?

Answer:

Step 1 of 2

Given, body temperatures of healthy adults have a bell-shaped distribution with a mean of 98.20°F and a standard deviation of 0.62°F. Using the empirical rule, what is the approximate percentage of healthy adults with body temperatures

a. within 1 standard deviation of the mean, or between 97.58°F and 98.82°F?

P()

= P(-1 < Z < 1)

= P(Z < 1) - P(Z < - 1)

= 0.8413 - 0.1587

= 0.6826

Therefore, approximate percentage of healthy adults with body temperatures between 97.58°F and 98.82°F is 68.26%.