Assume that human body temperatures are normally distributed

Assume that human body temperatures are normally distributed with a mean of 98.2

Solution

bottom 2%:

P(X<x)=0.02

--> P((X-mean)/s <(x-98.2)/0.62) =0.02

--> P(Z<(x-98.2)/0.62) =0.02

--> (x-98.2)/0.62= -2.05 (from standard normal table)

So x= 98.2-2.05*0.62 =96.929

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top 2%:

P(X>x)=0.02

--> P((X-mean)/s <(x-98.2)/0.62) =1-0.02=0.98

--> P(Z<(x-98.2)/0.62) =0.98

--> (x-98.2)/0.62= 2.05 (from standard normal table)

So x= 98.2+ 2.05*0.62 =99.471