Question

The body temperatures of a group of healthy adults have a bell-shaped distribution with a mean of 98.35°F and a standard deviation of 0.64°F. Using the empirical rule, find each approximate porcent
a. What is the approximate percentage of healthy adults with body temperatures within 3 standard deviations of the mean, or between 96.43°F and 100.27°F?

b. What is the approximate percentage of healthy adults with body temperatures between 97 71°F and 98.99°F?

a. Approximately % of healthy adults in this group have body temperatures within 3 standard deviations of the mean, or between 96.43°F and 100.27°F

(Type an integer or a decimal. Do not round)

Answer 1

Answer:

a) 99.97%

b) 65%

Step-by-step explanation:

• 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ.

• 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.

• 99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.

Mean of 98.35°F and a standard deviation of 0.64°F.

a. What is the approximate percentage of healthy adults with body temperatures within 3 standard deviations of the mean, or between 96.43°F and 100.27°F?

μ - 3σ

98.35 - 3(0.64)

= 96.43°F

μ + 3σ.

98.35 + 3(0.64)

= 100.27°F

The approximate percentage of healthy adults with body temperatures is 99.97%

b. What is the approximate percentage of healthy adults with body temperatures between 97 .71°F and 98.99°F?

within 1 standard deviation from the mean - that means between μ - σ and μ + σ.

μ - σ

98.35 - (0.64)

= 97.71°F

μ + σ.

98.35 + (0.64)

= 98.99°F

Therefore, the approximate percentage of healthy adults with body temperatures between 97.71°F and 98.99°F is 65%