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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?