Answer to Question #350368 in Statistics and Probability for Cel

Question

Scores of an achievement test show that it follows a normal distribution. Its mean is 79 with a

standard deviation of 8. Find the probability that students’ scores will be higher than the passing score

of 70.

Answer 1

We have a normal distribution, $\mu=79, \sigma=8.$

Let's convert it to the standard normal distribution,

$z=\cfrac{x-\mu}{\sigma}=\cfrac{70-79}{8}=-1.13;$

$P(X>70)=P(Z>-1.13)=1-P(Z<-1.13)=\\ =1-0.1292=0.8708\ \text{​(from z-table).}$