Assume that human body temperatures are normally distributed with a mean of 98.1

Question

Assume that human body temperatures are normally distributed with a mean of 98.18 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.) Click to view page 1 of the tabie, 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.)

Explanation / Answer

a) P(X < 100.6) = P((X - mean)/sd < (100.6 - mean)/sd)

                          = P(Z < (100.6 - 98.18)/0.62)

                          = P(Z < 3.9)

                          = 1 = 100%

As the probability is greater than 0.95, so the cutoff score 100.6 is not appropriate.

b) P(X > x) = 0.05

or, P((X - mean)/sd > (x - 98.18)/0.62) = 0.05

or, P(Z > (x - 98.18)/0.62)) = 0.05

or, P(Z < (x - 98.18)/0.62)) = 0.95

or, (x - 98.18)/0.62 = 1.645

or, x = 1.645 * 0.62 + 98.187

or, x = 99.21

So the minimum temprature is 99.21

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