Question

Assume that human body temperatures are normally distributed with a mean of 98.21°F and a standard deviation of 0.64°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 100.6F 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

Answer 1

SOLUTION:

Solution :

Given that ,

mean = $\mu$ = 98.21

standard deviation = $\sigma$ =0.64

P(x <100.6 ) = P(( x -$\mu$) / $\sigma$ (100.6-98.21) / 0.64)

= P(z <3.73 )

Using z table

= 0.9999

=99.99%

B.

Using standard normal table,

P(Z > z) = 5%

= 1 - P(Z < z) = 0.05  

= P(Z < z) = 1 - 0.05

= P(Z < z ) = 0.95

= P(Z < 1.65 ) = 0.95  

z =1.65

Using z-score formula,

x = z * $\sigma$ + $\mu$

x = 1.65 * 0.64+98.21

x = 98.266

=98.27