If x is normally distributed with mean µ and standard deviation σ, and given that the probability that x is less than 32 is 0.0228, find the value of µ.

Answer 1

z = (mean - mu)/sigma

probability of 0.228 corresponds to z = -2

-2 = (mean - mu)/sigma

-2*sigma = mean - mu

2*sigma = mu - mean

2*sigma + mean = mu