The time of arrival of an employee in his office is a random variable uniformly distributed between 8:45 and 9:15 AM. At the end of every 100 work days if the average of the arrival times is over 9:03, the employee pays a fine. 1. By using the CLT determine the probability that the employee will be fined. Note that in this model coming early on one day compensates for coming late on another day. 2. If the employer changes the policy and only averages on the late days (days that the employee arrives after 9:00 AM) what is the probability that the employee will be fined? (Note that in this case, being early on one day does not help being late on another day, in other words, being early is like arriving at 9:00 AM.)