Assume that human body temperatures are normally distributed with a mean of 98.2
ID: 3226169 • Letter: A
Question
Assume that human body temperatures are normally distributed with a mean of 98.20 degrees F and a standard deviation of 0.61 degree F. a. A hospital uses 100.6 degree 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 degree 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.)Explanation / Answer
Mean = 98.2 degree F
Standard deviation = 0.61 degree F
a) Percentage of normal and healthy persons to be considered to have fever = P(X>100.6)
= 1 - P(X<100.6)
= 1 - P(Z < (100.6 - mean)/standard deviation)
= 1 - P(Z < (100.6 - 98.2)/0.61)
= 1 - P(Z < 3.93)
= 1 - 0.99996
= 0.00004
The cut off includes very much less than 5% of total population and hence, it is appropriate
b) Let the minimum temperature for top 5% be x
P(Z < (X - 98.2)/0.61) = 0.05
(X - 98.2)/0.61) = 1.645
X = 99.2 degree F