Question

Determine Z and X values for a given probability. Z is standard normal, X is normal.

Given

      μ = 12 (Units not given)

      σ = 3.2 (Units not given)

      The probability in the upper tail is:

      α = 0.095 (Unitless)

Determine the Z Value associated with the probability and calculate the X Value associated with the Z value.

Answer 1

Given that, mean = 12 and standard deviation = 3.2

We want to find, z-score such that,

P(Z > z) = 0.095

=> 1 - P(Z < z) = 0.095

=> P(Z < z) = 0.905

Using standard normal z-table we get, z-score corresponding probability 0.905 is z = 1.31

=> Z = 1.31

=> X = 16.192