Math Problem Statement

Assume that human body temperatures are normally distributed with a mean of 98.22°F and a standard deviation of

0.62°F.

A hospital uses 100.6°F as the lowest temperature considered to be a fever. What percentage of normal and healthy persons would be considered to have a fever? Does this percentage suggest that a cutoff of 100.6°F is appropriate?

Physicians want to select a minimum temperature for requiring further medical tests. What should that temperature be, if we want only 5.0% of healthy people to exceed it? (Such a result is a false positive, meaning that the test result is positive, but the subject is not really sick.)

Click to view page 1 of the table. Click to view page 2 of the table.

a. The percentage of normal and healthy persons considered to have a fever is (Round to two decimal places as needed.)

%.

Solution

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Math Problem Analysis

Mathematical Concepts

Normal Distribution
Z-score
Probability
False Positives

Formulas

Z-score formula: z = (x - μ) / σ
Percentile calculation using Z-scores

Theorems

Properties of the Normal Distribution
68-95-99.7 Rule

Suitable Grade Level

Grades 10-12