Question

The heights of the population of boys are normally distributed with a mean of 66 inches and al standard deviation of 8.9 inches. If a random sample of 40 boys is drawn from this population, what is the probability that the mean of this sample is greater than 64.5 inches?

Answer 1

$Z=\frac{x-\mu}{s/\sqrt{n}}=\frac{64.5-66}{8.9/\sqrt{40}}=-1.07$

P(64.5<Z<66)=0.14231

P(Z>66)=0.5

P(Z>64.5)=0.5+0.14231=0.64231