Let x be normal random variable with a standard deviation of

Let x be normal random variable with a standard deviation of 5. What is the mean of x if P(x>36)=0.1151?

Solution

If P(x>36) = 0.1151, then the corresponding z score to it, using table/technology, is

z = 1.199843825

Thus, as

u = x - z*s

Then

u = 36 - 1.199843825*5 = 30.00078088 [ANSWER]