6.44 Is the die balanced? A balanced die with six sides is rolled 60 times.

a. For the binomial distribution of X = number of 6s, what is n and what is p?

b. Find the mean and the standard deviation of the distribution of X. Interpret.

c. If you observe x = 0, would you be skeptical that the die is balanced? Explain why, based on the mean and standard deviation of X.

d. Show that the probability that x = 0 is 0.0000177.