The mean cost of a five pound bag of shrimp is 46 dollars wi

The mean cost of a five pound bag of shrimp is 46 dollars with a variance of 64. If a sample of 51 bags of shrimp is randomly selected, what is the probability that the sample mean would differ from the true mean by more than 2.6 dollars

Solution

The probability is

P(|xbar-mean|>2.6) = P(xbar-mean<-2.6) + P(xbar-mean>2.6)

=P((xbar-mean)/(s/vn) <-2.6/sqrt(64/51)) + P((xbar-mean)/(s/vn) >2.6/sqrt(64/51))

=P(Z<-2.32)+P(Z>2.32)

=0.0203 (from standard normal table)