Fairness of a die. Perform a similar experiment to the one described in Exercise 24.4, but replace the coin with a fair die. Roll the die until you are 95% confident that the mean value is...

Fairness of a die. Perform a similar experiment to the one described in Exercise 24.4, but replace the coin with a fair die. Roll the die until you are 95% confident that the mean value is (1+2+3+4+5+6)/6 = 3.5 within 0.05. How many rolls did it take? (It will be faster to simulate your die with a PNRG.) Use Student’s t-distribution for an infinite number of degrees of freedom when computing the confidence intervals. Are you also confident that the die is fair — that is, are all sides equally likely? If not, explain how you could be.