The number of passengers arriving at a particular bus stop is Poisson distributed with a mean rate of 1.2 passengers per minute.
1. Calculate the probability that more than 4 passengers arrive in the next 3 minutes.
2. Calculate the expected number of passenger arrivals in a 5 minutes interval. Also, calculate the standard deviation of the number of arrivals in 5 minutes.
3. If we are told that 15 passengers have arrived between 7:00 A.M and 7:10 AM, calculate the probability that 10 out if 15 passengers arrived in the last 5 minutes L Lg, between 7:05 AM and 7:10 AM)