Assume that human body temperatures are normally distributed with a mean of 98.2
ID: 3231709 • Letter: A
Question
Assume that human body temperatures are normally distributed with a mean of 98.20 degree 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 cut off 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 false positive, meaning that the test result is positive, but the subject is not really sick.) a. The percentage of normal and healthy persons considered to have a fever is % (Round to two decimal places as needed.) Does this percentage suggest that a cutoff of 100.6 degree F is appropriate? A. Yes, because there is a large probability that a normal and healthy person be considered to have a fever. B. Yes, because there is a small probability that a normal and healthy person would be considered to have a fever. C. No, because there is a small probability that a normal and healthy person would be considered to have a fever. D. No, because there is a large probability that a normal and healthy person would be considered to have a fever. b. The minimum temperature for requiring further medical tests shul be degree F if we want only 5.0% of healthy people to exceed it (Round to two decimal places as needed.)Explanation / Answer
a) P(X>100.6)=1-P(Z<(100.6-98.20)/0.61)=1-P(Z<3.9344)=1-1=0.0000~00.00%
b)option B is correct
b)for top 5%; z=1.645
hence corresponding temperature =98.2+1.645*0.61=99.2