Assume that human body temperatures are normally distributed with a mean of 98.18 degrees F and a standard deviation of 0.62 degrees F

Question

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

Assuming temperature is a normal distribution. Can use Standard normal (z) curves.

The mean is 98.18 and the standard deviation is 0.62. The cutoff is 100.6.

The z value is the difference of the cutoff minus the mean divided by the standard deviation.

z = (100.6 - 98.18)/ 0.62 = 3.9

Found the Standard normal (z) curve a z of 3.9 is basically 1.0000 or 100.00%.

This means there are no false positives and probably a lot of false negatives. The cutoff is too high.

With 5.0% false positives allowed, to find the new cutoff first have to determine the z value for 100.0% - 5.0%.

From the Standard normal (z) curve we find that 95.0% is 1.645.

1.645 = (new cutoff - 98.18)/0.62. Yields 1.645 x 0.62 = new cutoff - 98.18 = 1.02 = new cutoff - 98.18

New cutoff = 1.02 + 98.18. New cutoff equals 99.2 degrees Fahrenheit.