Question

The scores received by students completing a geology exam are normally distributed. If the average score is 122 and the standard deviation is 35, what percentage of students scored between 52 and 122?

Answer 1

Notice that $52=122-70=122-2\times35$, so the probability is equivalent to

$\mathbb P(-2$

where $Z$ follows the standard normal distribution. This is half the proportion of the students that fall within two standard deviations of the mean:

$\mathbb P(-2$

Recall the empirical rule, which states that approximately 95% of a normal distribution falls within two standard deviations of the mean. This means that

$\mathbb P(-2$

of students scored between 52 and 122.