The wildlife department has been feeding a special food to r

The wildlife department has been feeding a special food to rainbow trout fingerlings in a pond. Based on a large number of observations, the distribution of trout weights is normally distributed with a mean of 402.7 grams and a standard deviation 8.8 grams. What is the probability that the mean weight for a sample of 40 trout exceeds 405.5 grams?

Solution

P(xbar>405.5) = P((xbar-mean)/(s/vn) >(405.5-402.7)/(8.8/sqrt(40)))

=P(Z>2.01)

=0.0221 (from standard normal table)