The duration of a consult appointment for diabetes at a particular Endocrinology clinic follows a normal distribution with a mean of 45 minutes and a standard deviation of 10 minutes. The duration of a follow-up appointment also follows the normal distribution with a mean of 20 minutes and a standard deviation of 10 minutes. The clinic operates for 8 hours from 8 am to 4 pm without a lunch break. There are 8 consult appointments and 4 follow-up appointments that must be booked the next day. Assume that the appointments are independent of each other.

a) Define a random variable that contains the total duration of consult and follow-up appointments combined. What is the distribution of this random variable? Explain. b) What is the mean and standard deviation of the total duration of consult and follow-up appointments combined? c) Calculate the probability that all the appointments for the next day will be completed by 4 pm and the clinic does not have to go overtime. d) Does the sequence of consult and follow-up appointments impact the probability you calculated in part (c)? explain.