Question

The scores on a national achievement exam are normally distributed with a mean of 600 and a standard deviation of 120. If a student is selected at random, find the probability that the student scored above 660

Answer 1

Since $\mu=600$ and $\sigma =120$ we have:

$P (X>660) = P(X-\mu>660-600) = P(\dfrac{X-\mu}{\sigma}-\dfrac{660-600}{120})$

Since $\dfrac{X-\mu}{\sigma}$ and $\dfrac{660-600}{120}$ = 0.5 we have:

P(X > 660) = P(Z > 0.5)

Use the standard normal table to conclude that:

P(Z > 0.5) = 0.3085