Normal Approximation to the Binomial Distribution. The UCSB parking manage- ment knows that 89% of parking tickets are paid on-time. The fine, when paid on-time is $25. Over Halloween weekend, UCSB parking management issued 312 parking tickets. (i) Find the mean and standard deviation of the number of these tickets that will be paid in-full and on time.
(ii) Find the mean and standard deviation of the of the amount of money that will be generated from payment of the tickets.
(iii) What is the probability that at most 290 tickets are paid on-time? (Hint: use the normal approximation for the binomial distribution).