Need correct answer with detailed calculation

People arrive at a voting precinct according to a Poisson Process {N(t), t 0} with a rate people per hour. Assume that the venue opens at 7:00 a.m. and that no one is waiting outside the venue at that time (that is, 7:00 a.m. is time t = 0). Answer the following questions.

(a) It is known that between 9:45 and 10:45, 80 people arrived at the site, what is the probability that 120 arrived between 9:30 and 11:00?

(b) Calculate the probability that 70 or more people have arrived between 12:30 and 13:30, if it is known that between 12:00 and 13:00 55 people arrived at the venue.

(c) Consider that it is 8:30 and that the last person who arrived was 5 minutes ago. Calculate the expected time until the next person arrives.

(d) Assume the arrival time of the 22nd person was less than or equal to 1.5 hours from when the venue opened. What is the probability that 15 people will arrive in the first hour after the venue opens?