# Probability Z-Scores - need help with problems?

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.

i) Find the probability that the average score of this group of students is higher than the average (i.e., 75).

ii) Find the probability that the sample mean deviates from the population mean by more than 1.5.

So for i) I'm a little confused because I assumed you would have to use the z score. But since x would be 75, it would be z = (75 - 75)/0.57 and that gives 0? That can't be the right probability, can it?

I straight up don't understand how to do ii). I would appreciate some help!

### 1 Answer

- Mike GLv 75 months agoFavorite Answer
μ = 75

σ^2 = 16

σ = 4

n = 50

i) z(X=75) = (75-75)/(4/√50) = 0

P(z>0) = 0.5000

ii) 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

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