Question

Healthy people have body temperatures that are normally distributed with a mean of 98.20∘F and a standard deviation of 0.62∘F.
(a)  If a healthy person is randomly selected, what is the probability that he or she has a temperature above 99.1∘F?
answer:  
(b)  A hospital wants to select a minimum temperature for requiring further medical tests. What should that temperature be, if we want only 1 % of healthy people to exceed it?

answer:

Answer 1

Solution :

Given ,

mean = = 98.20

standard deviation = = 0.62

P(x >99.1 ) = 1 - P(x<99.1 )

= 1 - P[(x -) / < (99.1-98.20) /0.62 ]

= 1 - P(z <1.45 )

Using z table

= 1 - 0.9265

= 0.0735

probability= 0.0735

2.

Using standard normal table,

P(Z < z) = 1%

=(Z < z) = 0.01

z = -2.33   

Using z-score formula  

x = z +

x = -2.33 *0.62+98.20

x = 96.7554