Question

A distribution of values is normal with a mean of 87.6 and a standard deviation of 39.3.

Find P₂₅, which is the score separating the bottom 25% from the top 75%.
P₂₅ =

Enter your answer as a number accurate to 4 decimal places.

Answer 1

Here we need to find x such that $P(X<x)=0.25$

Using standard normal table we get $P(z<-0.674)=0.25$

So $z=-0.674=\frac{x-\mu}{\sigma}$

Hence $x=-0.674*\sigma+\mu=(-0.674*39.3)+87.6=61.1118$