Question

16. Assume that human body temperatures are normally distributed with a mean of 98.22°F and a standard deviation of 0.64°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.)

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 degrees Upper F is​ appropriate?

A. No, because there is a large probability that a normal and healthy person would be considered to have a fever.

B. No, because there is a small probability that a normal and healthy person would be considered to have a fever.

C. Yes, because there is a small probability that a normal and healthy person would be considered to have a fever.

D. ​Yes, 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 should be _____ F if we want only​ 5.0% of healthy people to exceed it.

​(Round to two decimal places as​ needed.)

Answer 1

Given:-

Assume that human body temperatures are normally distributed with a mean of 98.22°F and a standard deviation of 0.64°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?

No, this percentage does not suggest that a cutoff of 100.6°F is​ appropriate because probability is too small.

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?

Find the z-score tht has a right tail of 5%: z = inv(0.95) = 1.645

Find the temperature that corresponds to z = 1.645

  
  

99.27 degrees should be the temperature​, if we want only​ 5.0% of healthy people to exceed​ it.

A. The percentage of normal and healthy persons considered to have a fever is 0.001%

Does this percentage suggest that a cutoff of 100.6 degrees Upper F is​ appropriate?

No, because there is a small probability that a normal and healthy person would be considered to have a fever.

The minimum temperature for requiring further medical tests should be 99.27 F if we want only​ 5.0% of healthy people to exceed it.