Math Problem Statement

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

Question list

Question 11

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.)

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Question 12

Question 13

cents

Question 14

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¾ Question 15

a. The percentage of normal and healthy persons considered to have a fever is 0.006 %.

(Round to two decimal places as needed.)

Does this percentage suggest that a cutoff of 100.6°F is appropriate?

A. No, because there is a small probability that a normal and healthy person would be considered to have a fever.

B. Yes, because there is a large probability that a normal and healthy person would be considered to have a fever.

• c. No, because there is a large probabilty that a normal and healthy person would be considered to have a fever.

D. Yes, because there is a small probability that a normal and healthy person would be considered to have a fever.

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• Question 16

b. The minimum temperature for requiring further medical tests should be °F if we want only 5.0% of healthy

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people to exceed it.

(Round to two decimal places as needed.)

Solution

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Math Problem Analysis

Mathematical Concepts

Normal Distribution
Probability
Z-Score

Formulas

Z-score formula: z = (x - μ) / σ
Cumulative probability from z-score

Theorems

68-95-99.7 Rule for Normal Distribution
Standard Normal Distribution Theorem

Suitable Grade Level

Grades 11-12