Assume that human body temperatures are normally distributed with a mean of 98.1
ID: 3256260 • Letter: A
Question
Assume that human body temperatures are normally distributed with a mean of 98.19 degrees°F and a standard deviation of 0.61°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.)
Explanation / Answer
ans=
100.6 - 98.19 = 2.41.
Since 1 SD = 0.61,
2.41 / 0.61 = 3.95 SD.
Looking 3.95 SD up in a normal probability table, the probability a normal and healthy person has this temperature is very small, under .01%, or 1 in 10,000.
95% would equate
z = 1.644853627
As x = u + z * s,
where
u = mean = 98.19
z = the critical z score = 1.644853627
s = standard deviation = 0.61
Then
x = critical value = 99.22