1. ## Normal distribution intervals.

An instructor has two classes, one size 30, the other size 64. From past experience, the students' mean exam score is 77 and standard deviation is 15.
What is the approximate probability that the average test score in the size 30 class is more than 1 point higher than that of the size 64 class.

This is what I have so far but don't know where to go after this:
$\displaystyle P(X_{30} > X_{64} + 1) = P(\frac{X_{30}-77}{15/\sqrt{30}} > \frac{X_{64}-77}{15/ \sqrt{64}} + ?)$

2. Originally Posted by BERRY
An instructor has two classes, one size 30, the other size 64. From past experience, the students' mean exam score is 77 and standard deviation is 15.
What is the approximate probability that the average test score in the size 30 class is more than 1 point higher than that of the size 64 class.

This is what I have so far but don't know where to go after this:
$\displaystyle P(X_{30} > X_{64} + 1) = P(\frac{X_{30}-77}{15/\sqrt{30}} > \frac{X_{64}-77}{15/ \sqrt{64}} + ?)$
The mean class scores have means $\displaystyle 77$, and and variances $\displaystyle 15^2/30$ and $\displaystyle 15^2/64$ respectivly.

Therefore the difference in means has mean $\displaystyle 0$ and variance $\displaystyle 15^2/30+15^2/64$.

Now we want to know what is the probability (assume the difference is normall distributed) that a RV $\displaystyle X \sim N(0, 15^2/30+15^2/64)$ is greater than $\displaystyle 1$.

CB