Suppose X is a normally distributed random variable with the mean u(Mu) and variance sigma^2. Suppose P(X </= 10) - .6915 and P (X </= 20) -.8413. Find Mu and Sigma^2.

Question

PLEASE HELP! THIS IS AN EXAM REVIEW QUESTION!

Answer 1

for z-scores,
z = (x - m)/s

from my charts, a prob of .6915 corresponds to a z-score of .5
so .5 = (10 - m)/s
.5s = 10-m
m = 10 - .5s

and a prob of .8413 corresponds to a z-score of .9998 or 1
1 = (20-m)/s
s= 20-m
m = 20 - s

then 20 - s = 10 - .5s
s = -10/-.5 = 20
m = 0

If I recall variance is the square of the standard deviation.

I checked my answers with

http://davidmlane.com/hyperstat/z_table.html