Assume that human body temperatures are normally distributed with a mean of 98.2
ID: 3151818 • Letter: A
Question
Assume that human body temperatures are normally distributed with a mean of 98.21 degrees Upper F98.21°F and a standard deviation of 0.64 degrees Upper F0.64°F. a. A hospital uses 100.6 degrees Upper F100.6°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 degrees Upper F100.6°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
Assume that human body temperatures are normally distributed with a mean of 98.21 degrees Upper F98.21°F and a standard deviation of 0.64 degrees Upper F0.64°F. a. A hospital uses 100.6 degrees Upper F100.6°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 degrees Upper F100.6°F is appropriate?
Z value for 100.6, z=(100.6-98.21)/0.64 =3.73
P( x >100.6) =P( z >3.73)
= 0.0001
The required percentage =0.0001*100
=0.01%
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.)
z value for top 5% =1.645
x =98.21+1.645*0.64 = 99.2628
minimum temperature =99.26 F ( two decimals)