Suppose you roll a fair six-sided 50 times and calculate the mean roll, x.

a) We can consider these 50 rolls as an SRS of rolls from the population of all possible rolls of this die. We can determine that if the die is fair, the mean of this population is 3.5 and the standard deviation is 1.71. What is the shape of the population distribution?

b) Suppose that the mean of your 50 rolls is x = 3.25. Are you suspicious about the fairness of the die? Justify your answer using NormalCDF.