Assume that human body temperatures are normally distributed

Assume that human body temperatures are normally distributed with a mean of 98.19 degrees Upper F98.19°F and a standard deviation of 0.64 degrees Upper F0.64°F.
a. A hospital uses 100.6 degrees Upper F100.6°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 degrees Upper F100.6°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
nothing%.
(Round to two decimal places as needed.)
Does this percentage suggest that a cutoff of 100.6 degrees Upper F100.6°F is appropriate?
A.No, 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 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 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
???degrees Upper F°F if we want only 5.0% of healthy people to exceed it.
(Round to two decimal places as needed.)

Solution

a)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    100.6      
u = mean =    98.19      
          
s = standard deviation =    0.64      
          
Thus,          
          
z = (x - u) / s =    3.765625      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   3.765625   ) =    0.0000830665 or 0.00830665% [ANSWER]

OPTION C:

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

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b)

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.95      
          
Then, using table or technology,          
          
z =    1.644853627      
          
As x = u + z * s,          
          
where          
          
u = mean =    98.19      
z = the critical z score =    1.644853627      
s = standard deviation =    0.64      
          
Then          
          
x = critical value =    99.24270632   [ANSWER]

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