Question

In a Science test, the mean score is 42 and the standard deviation is 5. Assuming the scores are normally distributed, what percent of the score is:

Less than 50?

Answer 1

We have a normal distribution, $\mu=42, \sigma=5.$

Let's convert it to the standard normal distribution,

$z=\cfrac{x-\mu}{\sigma}=\cfrac{50-42}{5}=1.60;\\ P(X<50)=P(Z<1.60)=\\ =0.9452=94.52\% \text{ (from z-table).}$