
Statistics Quiz. Case 2. Explanation.
If you randomly put 480 objects into 12 boxes, it is highly unlikely that all of the boxes would have the same number of objects. A program that we wrote to do this gave us the following maximum in one box on 100 consecutive tries: 47, 49, 57, 59, 47, 43, 45, 47, 58, 50, 57, 48, 48, 53, 52, 43, 48, 53, 48, 51, 56, 49, 49, 48, 50, 57, 56, 51, 46, 48, 55, 48, 45, 45, 55, 54, 44, 46, 48, 52, 48, 51, 50, 49, 47, 46, 44, 46, 45, 51, 44, 46, 42, 53, 51, 49, 49, 51, 47, 46, 47, 50, 46, 49, 52, 54, 54, 54, 51, 51, 51, 48, 51, 44, 50, 48, 49, 50, 49, 49, 48, 50, 49, 60, 54, 57, 55, 54, 54, 46, 54, 50, 49, 52, 50, 50, 58, 48, 51, 52. In 50 out of these 100 random attempts, at least one box has at least 50 objects.
The probability that the box with the most objects contains at least 50 is not small. It would be surprising if you would get the same result for the same month in many different trials (for people born in different years, or different countries), but the fact that one of the months has 10 more people than the average is within expectations, according to the probabilities.
