All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.
Let X denote the number of people joining the queue in 4 minutes.
Let Y denotes number of people joining the queue in t seconds.
Using the Graphing Calculator, t = 55
Let W denote the number of people joining the queue in 15 minutes.
Let V denote the number of people leaving the queue in 15 minutes.
by continuity correction
The average number of people joining the queue per minute may not remain constant throughout a period of long hours as they have different traveling time. There might be no flight departing too. Thus, it would not appropriate.
The question is pretty standard Poisson. So long as students are careful with continuity correction, I don’t see much problems with this questions. They should answer (iv) contextually.