Assume that human body temperatures are normally distributed with a mean of 9823

Question

Assume that human body temperatures are normally distributed with a mean of 9823°F and a standard deviation of 0.63° 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 t? (Such a result is a 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 tat a atoff of 1006 is appropriate? A. Yes, because there is a small probability that a normal and healthy person would be considered to have a fever O B. No, because there is a small probability that a normal and healthy person would be considered to have a fever O C. Yes, because there is a large probability that a normal and healthy person would be considered to have a fever 0 D. No, because there is a large probability that a normal and healthy person would be considered to have a fever. rFwe want only 5.0% of healthy people to exceed t b, The minimum temperature for requiring further medical tests should be Round to two decimal places as needed.)

Explanation / Answer

a) % of those considered to have a fever is =P(X>100.6)=P(Z>(100.6-98.23)/0.63)=P(Z>3.7619)=0.01%

option A is correct

b)

for top 5% ; z =1.6449

hence corresponding temperature =mean +z*Std deviation =99.27 oF

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