Math Problem Statement

The body temperatures of a group of healthy adults have a​ bell-shaped distribution with a mean of 98.27degreesF and a standard deviation of 0.65degreesF. Using the empirical​ rule, find each approximate percentage below. a. What is the approximate percentage of healthy adults with body temperatures within 2 standard deviations of the​ mean, or between 96.97degreesF and 99.57degrees​F? b. What is the approximate percentage of healthy adults with body temperatures between 96.32degreesF and 100.22degrees​F? Question content area bottom Part 1 a. Approximately    enter your response here​% of healthy adults in this group have body temperatures within 2 standard deviations of the​ mean, or between 96.97degreesF and 99.57degreesF.

Solution

To solve this problem, we can use the Empirical Rule (or the 68-95-99.7 rule) which applies to bell-shaped, or normal, distributions. This rule states that:

  1. About 68% of the data falls within 1 standard deviation of the mean.
  2. About 95% of the data falls within 2 standard deviations of the mean.
  3. About 99.7% of the data falls within 3 standard deviations of the mean.

Part (a):

You are asked to find the percentage of healthy adults

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Math Problem Analysis

Mathematical Concepts

Normal distribution
Empirical rule

Formulas

-

Theorems

Empirical rule

Suitable Grade Level

Grades 10-12

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