Sampling distributions

Question

A manufacturer knows that their items have a normally distributed length, with a mean of 15.1 inches and standard deviation of 2.8 inches

if seven items are chosen at random, what is the probability that they are mean length is less than 17.7 inches

Answer 1

z = (17.7-15.1)/(2.8/sqrt(7)) = 2.45676907455998

P(Z <= 2.45676907455998) = , from Excel, normsdist(2.45676907455998) = 0.99299036144302, which can round to .9930.