Given Normal Distribution and probability, find mean

Question

If x is normally distributed with mean 𝜇 and standard deviation 𝜎 = 4 and given that the probability that x is less than 32 is 0.0228, find the value of 𝜇.

Answer 1

The z - value which correspondent to probability 0.0228 is -2.

(x-µ)/σ = -2 ------ eq 1

Here x= 32, σ = 4

Substituting the x and σ value in equation 1

(32-µ)/4 = -2

Now, we can calculate the value of µ

32 - µ = -8

µ = 32 +8 = 40

I hope this helps. If you have any question, please feel free to ask me in the comments section.