Download Probability and the distribution of sample means

Probability and the distribution of sample means
A large grocery store has received a shipment of 1000 cases of
oranges. The shipper claims that the cases average U = 40 oranges
with a standard deviation of 2. To check this claim, the store
manager randomly selects 4 cases and counts the number of
oranges in each case. For these 4 cases, the average number of
oranges is X = 38.
Assuming the shipper’s claim is true, what is the probability of
obtaining a sample mean this small? Is the store owner getting
ripped off?