Normal Distribution

Question

Assume that human body temperatures are normally distributed with a mean of 98.23°F and a standard deviation of 0.62°F.

a. 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?

b. 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.)

Answer 1

Answer 2

a. Using technology,

select probabilities given a normal distribution.

The mean is 98.23 and the standard deviation is .62. Given a 100.6 as the lowest temperature considered to be a fever, .0066% of normal and healthy persons would be considered to have a fever. This percentage suggests that a cutoff of 100.6 is inappropriate; it is too high.

b. If we want only 5.0% of healthy people to exceed it, the temperature should be 99.25