Five hundred people participate in a 12-week survey to see how many times that they go to a religious service. Each person's attendance has a Binomial distribution with n = 12 and p = 0.7. Assume that the people behave independently with regard to attendance.
a. What is the actual distribution of the number of religious services attended altogether during the 12-week period?
b. Estimate the probability that the 500 people attended between 4170 and 4230 religious services altogether during the 12-week period.