Assume that the human body temperatures are normally distributed with a mean of 98.22F and a standard deviation of 0.62F. A hospital uses 100.6F as the lowest temperature considered to be a fever.

Question

What percentage of normal and healthy persons would be considered to have a fever?

part 2:

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?

Answer 1

(a) Prob ( x > 100.6) =

1 - Prob ( x <= 100.6) =

1 - Prob ( z < = (100.6- 98.22)/0.62 )

= 1 - Prob ( z <= 3.8387)

= 1 - 0.999938

= 0.000062

0.0062% = 62/1000000 = 31/500000

(b) Prob ( Z < z) = 0.95 <--- must be 95% or less probability

So then z = 1.645

z = (x - mean)/stddev

z * stddev + mean = x

x = z * stddev + mean

= 1.645 * 0.62 + 98.22

= 99.24