Question

Solve by Poisson's distribution method. If it cannot be solved by that method then explain why.

Paolo has plans to meet his friend for lunch at noon. The trip will take him 12 minutes by bus, and buses run every 5 minutes. If he gets to the bus stop at 11:45, what is the probability that he will arrive on time to meet his friend?

Answer 1

The rate of arrival is one bus per 5 minutes.

There is 15 minutes remain when he gets to the bus stop at 11:45.

The trip will take him 12 minutes by bus.

So if the bus comes within 3 munits then he will arrive on time to meet his friend

Therefore the rate of arrival of bus in three minutes =t = 1*( 3/5) = 0.6

Let X = number of buses arrive in three munites.

We want to find probability of atleast one bus arrive within 3 minutes.

mathematically, we want to find P( X >= 1) = 1 - P( X = 0) .......( 1 )

Therefore P( X = 0) = 0.549

Plug this value in equation ( 1 ), we get

P( X >= 1) = 1 - 0.549 = 0.451 ( this is the final answer).