Sampling Distribution

The heights of women are normally distributed with a mean of 64 inches and a standard deviation of 2.

a) what is the probability that a randomly selected woman is taller than 66 inches?
b) A random sample of four women is selected. What is the probability that the sample mean height is greater than 66 inches?
c) What is the probability that the mean height of a random sample of 100 women is > than 66inches?

a) I got it down to P(z>1) = .5 - .341 = .1587
b) I got it down to P(z>2) = .5 - .4772 = .0228
c) need help

n = 100..
z= (66-64) / (2/sqrt(100)) = I get P(Z>10). am i doing this right? thanks for any help

a) correct

b) correct

c) bizzare question, but yes, your working is correct. The answer was probably be almost as close to 0 as you can get!