Question

EJ L
Assume that human body temperatures are normally distributed with a mean of 98.19°F and a standard deviation of 0.61°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.)
Click to view page 1 of the table. Click to view page 2 of the table.
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°F is appropriate?
OA. Yes, because there is a small 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 large probability that a normal and healthy person would be considered to have a fever.
D. No, 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.)
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Answer 1

The percentage of normal and healthy persons would be considered to have a​ fever is 0.00102%

What is Probability?

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

Human body temperatures are normally distributed with a mean of μ = 98⁰F and a standard deviation of σ = 0.61⁰F

A hospital uses 100.6°F as the lowest temperature considered to be a fever.

Let x be the random variable that represents the human body temperatures.

           Z = (x - μ) / σ

for x = 100.6°F

        Z = (100.6 - 98) / 0.61

        Z = 4.26

Using normal distribution table for z-values for right-tailed area ,

P(x > 100.6) = P(z > 4.26) = 0.00102%

Thus, the percentage of normal and healthy persons would be considered to have a​ fever is 0.00102%

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