Suppose that samples of size are selected at random from a normal population with mean 100 and standard deviation 10. What is the probability that the sample mean falls in the interval from to ?

I'm not sure if I did this correctly, have I made any mistakes?

$\displaystyle \sigma$x = $\displaystyle \frac{\sigma}{\sqrt{n}}$ = 2

then for the lower interval I get 100-2.2(2) = 95.6

and for the upper interval 100+1.2(2) = 102.4

So P(95.6 < X < 102.4) --> P((95.6 - 100)/2 < Z < (102.4-100)/2) -->

P(-2.2 < Z < 1.2) --> P(1.2) - P(-2.2) and from the Z chart

0.884930 - 0.013903 = 0.871027