Question

Human body temperatures are normally distributed with a mean of 98.6 and a standard deviation of 0.72.? How do I Find the temperature that separates the top 7% from the bottom 93%?

Answer 1

Temprature that separates top 7% from the bottom 93% is `99.67`

Explanation:

Look at the diagram -

Find the probability area bound by 93% or 0.93.
0.5 lies to the left of the mean value.
`0.93 - 0.5= 0.43` lies to the right of mean.
Find the corresponding `z` value for `0.43`.
It is 1.48.

Use this value to determine the required `x` value.
You have to use the formula -

`z=(x-mu)/sigma`

Solve it for `x`

`x=z *sigma + mu`

Where -

`x = ?`
`z=1.48`
`sigma=0.72`
`mu = 98.6`

Plug in these values in the formula-

`x=(1.48*0.72)+98.6 = 1.07+98.6=99.67`

Temprature that separates top 7% from the bottom 93% is `99.67`