statistics and probability

Question

A particular fruit's weights are normally distributed, with a mean of 768 grams and a standard deviation of 20 grams.

If you pick 15 fruit at random, what is the probability that their mean weight will be between 769 grams and 780 grams

Answer 1

P(769 < xbar < 780) =

P( (769 - 768)/(20/sqrt(15)) < z < (780 - 768)/(20/sqrt(15)) = P(0.19 < z < 2.32) = P(z < 2.32) - P(z < 0.19) - 0.9898 - 0.5753 = 0.4145