Question

Assume that human body temperatures are normally distributed with a mean of 98.23 Fahrenheit and a standard deviation of .61 Fahrenheit.

A. A hospital uses 100.6 Fahrenheit as of 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 Fahrenheit is appropriate?

B. Physicians want to select a minimum temperature for requiring further medical tests. What should the temperature be, if we want only 5.0% of healthy people to exceed it?

(A) The percentage of normal and healthy person is considered to have fever is(round to 2 decimal places as needed)

Does this percentage suggest that a cut off of 100.6 Fahrenheit is appropriate?

A. Yes 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 large 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 a healthy person would be considered to have a fever

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

B. The minimum temperature for requiring further medical test should be blank Fahrenheit if we were only 5.0% of healthy people to exceed it. Round to two decimal places as needed

Answer 1

A.:  a)
Percentage of persons with temperature in excess of 100.6:
μ = 98.23
σ = 0.61
standardize x to z = (x - μ) / σ
P(x > 100.6) = P( z > (100.6-98.23) / 0.61)
= P(z > 3.93) = 0.000032 (0.0032 %)

B. From the normal probability table, P( z > 1.645) = 0.05
z = (x - μ) / σ
1.645 =( x-98.23) / 0.61
x = (1.645)(0.61)+ 98.23 = 99.23 F

a)

The percentage of normal and healthy person is considered to have fever is.01% Yes, because there is a small probability that a normal and healthy person would be considered to have a fever.

b) if we were only 5.0% of healthy people to exceed it. then minimum temperature is99.23 F