How is the rejection region defined and how is that related to the z-score and the p value? When do you reject or fail to reject the null hypothesis? Why do you think statisticians are asked to...

1. The graduate selection committee wants to select the top 10% of applicants. On a standardized test with a mean of 500 and a standard deviation of 100, what would be the cutoff score for selecting the top 10% of applicants, assuming that the standardized test is normally distributed? z=1.28 
we want x1 such that P(x > x1 )= .1
P(x > x1 ) = P(z > z1) where z1 = ( x1-500)/100
Z1= 1.28
So x1...