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

(a) We can consider these 50 rolls as a SRS of rolls from the population of all possible rolls of this die. Using formulas from Chapter 6, we can determine that if the die is fair, the mean of this population is 3.5 and the standard deviation 1.71. How would you describe the shape of this population distribution?

(b) Find the shape, center, and spread of the sampling distribution of x .

(c) Suppose that the mean of your 50 rolls is x the die? Justify your answer