Question

In a math test,the mean score is 45 and the standard deviation is 4. Assuming normality, what is the probility that a score picked at random will kie above 50?

Answer 1

We have a normal distribution, $\mu=45, \sigma=4.$ Let's convert it to the standard normal distribution, $z=\cfrac{x-\mu}{\sigma}=\cfrac{50-45}{4}=1.25;$

$P(X>50)=P(Z>1.25)=1-P(Z<1.25)=1-0.8944=0.1056$ (from z-table).