Assume the human body temperatures are normally distributed with a mean of 98.18°F and a standard deviation of 0.63°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 cut off 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.)
See Negative and Positive Z scores
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 cut off of 100.6% is appropriate?
o A. No, because there is a small probability that a normal and healthy person would be considered to have a fever.
o B. Yes, because there is a small probability that a normal and healthy person would be considered to have a fever.
o C. No, because there is a large probability that a normal and healthy person would be considered to have a fever.
o 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)
Answers & Comments
Verified answer
a)
Percentage of persons with temperature in excess of 100.6:
μ = 98.18
σ = 0.63
standardize x to z = (x - μ) / σ
P(x > 100.6) = P( z > (100.6-98.18) / 0.63)
= P(z > 3.8413) = 0.000062 (0.0062 %)
(From Normal probability table)
Does this percentage suggest that a cut off of 100.6°F is appropriate? NO
b)
From the normal probability table, P( z > 1.645) = 0.05
z = (x - μ) / σ
1.645 =( x-98.18) / 0.63
x = (1.645)(0.63)+ 98.18 = 99.22 F
a)
0.0062 %
No, because there is a small probability that a normal and healthy person would be considered to have a fever.
b)
99.22 F