Question

Suppose X is a normal random variable where P(X > 4.04) = 0.8944 and P(X > 13.68) = 0.1230. Find the mean and the standard deviation of X.

Answer 1

Given P( X > 4.04) = 0.8944

So 4.04 - / = Z_{​​​​​​0.1056}

Z0.1056 is score corresponding to area to left 0.1056

Using Z table , Z_{​​​​​​0.1056} = -1.25

4.04- / = -1.25

= 4.04

Also for P( X > 13.68)= 0.1230

13.68 - = Z_{​​​​​​0.8770}

Using Z table Z_{​​​​​​0.8770} = 1.16

   = 1.16

   = 13.68

Solving this two equations

We get   = 9.04 and = 4

So mean = 9.04 and standard deviation = 4