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?
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