Question

A normal distribution has μ = 80 and σ = 10. What is the probability of randomly selecting between the mean and a score of 50

Answer 1

Since  $\mu$ =80 and  $\sigma=10$ we have

We need to compute  Pr(X≤50). The corresponding z-value needed to be computed is:

$Z= \frac{(x-mean)}{sd}$

At mean , $Z= \frac{(80-80)}{10}=0$

At x= 50, $Z= \frac{(50-80)}{10}=-3$

P(z<0)=0.

P(z<-3.00)=0.00135

P(z<−3.00)=0.00135

P(50<x<80) =P(z<0)−P(z<−3.00)

=0.5−0.00135

=0.4986