Q:

Find probability using Z-scores - don't understand solution

Graduate students applying for entrance to many universities must take a Miller Analogies Test. It is known that the test scores have a mean of 75 and a variance of 16. In 1990, 50 students applied for entrance into graduate school in physics. 
Find the probability that the sample mean deviates from the population mean by more than 1.5. 
So I'm trying to understand my teacher's solution for this but I'm having trouble seeing where some values are coming from. 
z = 1.5/(4/√50) = 2.6517 
P(z>2.6517) = 0.0040 
P(z<-2.6517) = 0.0040 
P = 0.0040+0.0040 = 0.0080
I get that the teacher is using the central limit theorem, but where did the values 0.0040 come from? I don't see it on the Z-score table. And I was also wondering why the teacher adds 0.0040+0.0040 at the end to get 0.0080.

A:

I have attached a possible $z$-score table, the percent of area from the mean to $z$ corresponding to $2.65$ is $49.6\% = 0.496$.
Hence $P(Z>2.6517) \approx 0.5-0.496 = 0.004$.
The final answer is added as can deviate from the mean by $1.5$ from either sides.

