Question

Suppose that the humidity of Atlanta area is normally distributed and
6.68% of all previous humidity records are equal to or below 42.5% humidity levels, and
77.45% of all previous humidity records are between 42.5% and 80% humidity levels
Using the information, find µ and (Sigma ^2) of this normal distribution for humidity levels in Atlanta area.
[Hint] Define: R.V. X = Humidity level of Atlanta area in records

Answer 1

let mean and std deviation are a and b

for 6.68 percentile and (77.45+6.68=84.13) percentile; crtiical z values are -1.5 and 1

therefore a-1.5b=42.5 ........(1)

a+b=80 .............(2)

solving above:

a =65

b=15

hence µ =65

and ² =15² =225