Normal Distribution Homework: Expectation and Variance for Sample of 25 Students

[Maybe_Memorie]

Homework Statement

Students of a US university have an average SAT score of 600 and a standard deviation of 75. Assume the scores are distributed as a normal distribution.

If X is the score of a randomly selected student, derive the expectation and variance of the mean score, Y, of n randomly selected students.

If the sample is of n=25 students, what is the probability Y exceeds 610?

Homework Equations

The Attempt at a Solution

For a normal distribution, the expectation is the mean, and the variance is the standard deviation squared, so am I correct in saying for n students it would be n times this value?

As for the second part, I'm lost

 

[Hammie]

excuse lack of latex code here.

from my general statistics book:

1. Yes, the mean of x(bar) is the population mean.
2. The standard deviation of the sample is sigma/sqrt(n).

You need to calculate the z score of 610. Then use this with standard tables, or calculator to find P(.67<Z<Infinity).