Solution Found!
The Empirical Rule Based on Data Set 3, body temperatures
Chapter 3, Problem 42BSC(choose chapter or problem)
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 \(98.20^{\circ} \mathrm{F}\) and a standard deviation of \(0.62^{\circ} \mathrm{F}\). 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 \(97.58^{\circ} \mathrm{F} \text { and } 98.82^{\circ} \mathrm{F}\)?
b. between \(96.34^{\circ} \mathrm{F} \text { and } 100.06^{\circ} \mathrm{F}\)?
Equation Transcription:
Text Transcription:
98.20°F
0.62°F
97.58°F and 98.82°F
96.34°F and 100.06°F
Questions & Answers
QUESTION:
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 \(98.20^{\circ} \mathrm{F}\) and a standard deviation of \(0.62^{\circ} \mathrm{F}\). 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 \(97.58^{\circ} \mathrm{F} \text { and } 98.82^{\circ} \mathrm{F}\)?
b. between \(96.34^{\circ} \mathrm{F} \text { and } 100.06^{\circ} \mathrm{F}\)?
Equation Transcription:
Text Transcription:
98.20°F
0.62°F
97.58°F and 98.82°F
96.34°F and 100.06°F
ANSWER:
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%.