Question

The examination results of a large group of students in Statistics are approximately normally distributed with a mean of 60 and a standard deviation of 9. If a student is chosen at random, what is the probability that his score is Below 45?

Answer 1

We have a normal distribution, $\mu=60, \sigma=9.$

Let's convert it to the standard normal distribution,

$z=\cfrac{x-\mu}{\sigma}=\cfrac{45-60}{9}=-1.67;\\ P(X<45)=P(Z<-1.67)=\\ =0.0475 \text{ (from z-table)}.$