Question

2. Assume that human body temperatures are normally distributed with a mean of 98.22°F and a standard deviation of 0.62°F.
Part 1:
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?  
The percentage of normal and healthy persons considered to have a fever is___?___ .
​(Round answer to nearest hundredth of a percent - i.e. 23.34%)

Does this percentage suggest that a cutoff of 100.6°F is​ appropriate? Enter the letter of the statement that best answers the question
A. ​No, because there is a large probability that a normal and healthy person would be considered to have a fever.
B.​ Yes, because there is a large 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. ​Yes, because there is a small probability that a normal and healthy person would be considered to have a fever.

Part 2:
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.)

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

Normal distribution: P(X < A) = P(Z < (A - mean)/standard deviation)

Mean = 98.22 ^oF

Standard deviation = 0.62 ^oF

Part 1

P(X > 100.6) = 1 - P(X < 100.6)

= 1 - P(Z < (100.6 - 98.22)/0.62)

= 1 - P(Z < 3.84)

= 1 - 0.9999

= 0.0001

The percentage of normal and healthy persons considered to have a fever is 0.01

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

Part 2

Let the minimum temperature for requiring further medical tests be M

P(X > M) = 0.05

P(X < M) = 0.95

P(Z < (M - 98.22)/0.62) = 0.95

Take Z value corresponding to 0.95 from standard normal distribution table

(M - 98.22)/0.62 = 1.645

M = 99.24^oF

The minimum temperature for requiring further medical tests should be 99.24 °F if we want only​ 5.0% of healthy people to exceed it