Question

X is normally distributed with mean 50 and standard deviation 8. What value of X is such that only 8% of values are below it?

Answer 1

Mean = 50

Standard deviation = 8

p-value = 8% or 0.08

Firstly needs to find Z value using p-value from normal distribution table.

The value of X is such that only 8% of values are below mean, so p-value is:

= 1 - 0.08 = 0.92

Then the standardize value is:

Z = -1.41

$Z=\frac{\mu-x}{\sigma}$

$-1.41=\frac{x-50}{8}$

$x-50=-1.41\times8$

$x=-11.28+50=38.72$

This means approximately 8% of values are below the mean.