The SAT scores of entering freshmen at University X have a N

The SAT scores of entering freshmen at University X have a N (1200, 90) distribution and the SAT scores of entering freshmen at University Y have a N (1215,110) distribution. A random sample of 100 freshmen is sampled from each University, with the sample mean of the 100 scores from University X and the sample mean of the 100 scores from University Y. The probability that is greater than , the population mean for University Y, is

c. 0.0475. This answer is correct. has a N (1200, 90/ ) distribution. You now need to evaluate P( = 1215), since µy =1215. The result is 0.0475.

How do you find this answer? Please show work

Solution

This uses the Z-Test formula where

µ = 1200,

= 90,

N=100 and

Xbar = 1215
SE = standard error of the mean = /N
In this case,

Z = (Xbar - µ)/SE

z = ( 1215 - 1200 ) / (90 /10)
Z = 1.67
which indicates p(Xbar 1215) = 1 - 0.9525 = 0.0475 Answer