Question

A die is rolled 100 times. The total number of spots is 368 instead of the expected 350. Can this be explained as a chance variation, or is the die loaded?

A die is rolled 1000 times. The total number of spots is 3680 instead of the expected 3500. Can this be explained as a chance variation, or is the die loaded?

Answer 1

Let T show the total number of stops in 100 rolls. According to Central limit theorem, sampling distribution of sample sum will be approximately normal distribution with following parameters