A fair die is rolled 100 times. Using central limit theorem, estimate the probability that the sum of the faces is at least 360.
(a) A die is rolled 100 times and the number 6 appears 20 times. A statistician believes that the die may be loaded (i.e., not fair). Compute the probability that the number 6 would appear at least 20 times under the assumption that the die is fair. Use a normal approximation.
(b) The statistician then felt that the number of trials in (a) is too small and decided to observe further. Assume that in 1000 rolls of the die, the number 6 appears 200 times. Now compute the probability that 6 would appear at least 200 times under the assumption that the die is fair. Should the statistician now believe that the die is loaded? Why?