A study of 200 apple trees showed that the average number of

A study of 200 apple trees showed that the average number of apples per tree was 800. The standard deviation of the population is 100. What is the 95% confidence interval for the mean number of apples for all trees?

Solution

Given a=1-0.95 =0.05, Z(0.025) = 1.96 (from standard noraml table)

So the lower bound is

xbar - Z*s/vn =800-1.96*100/sqrt(200) =786.1407

So the upper bound is

xbar + Z*s/vn =800+1.96*100/sqrt(200) =813.8593