The Bureau of Infrastructure, Transport, and Regional Economics’ Domestic Airline On-Time Performance Reports identified that for “January 2018, on time performance over all routes operated by participating airlines (Jetstar, Qantas, QantasLink, Regional Express, Tigerair Australia, Virgin Australia and Virgin Australia Regional Airlines) averaged 85.0 per cent for on time arrivals and 85.1 per cent for on time departures.” On-time departures for Qantas were 87.0 per cent. The Qantas site states that in “accordance with industry standards, we measure an 'on-time' departure as one that departs the gate within 15 minutes of the scheduled departure time.”

a) Let X represent the number of Qantas departures in a random sample of 30 that depart on-time. What probability distribution does X follow? Justify your answer

b) What is the probability that at least 28 flights (i.e., 28 or more) of the random sample of 30 depart on-time. Show your calculations and include screenshots if using the online resource StatStar.