Question

In a Math test, the mean score is 42 and the standard deviation is 3. Assuming normality, what is the probability that the score picked will lie above score 50? *

Answer 1

We have a normal distribution, $\mu=42, \sigma=3.$

Let's convert it to the standard normal distribution,

$z=\cfrac{x-\mu}{\sigma}=\cfrac{50-42}{3}=2.67;$

$P(X>50)=P(Z>2.67)=\\=1-P(Z<2.67)=$

$=1-0.9962=0.0038$ ​(from z-table).