Solve the following (a) Suppose telephone calls arrive at an emergency hotline a

Question

Solve the following (a) Suppose telephone calls arrive at an emergency hotline at a rate of 3 per hour, and you begin monitoring calls at 12: 00 pm. Find the probability that the first call arrives after 2.00 pm. (b) A commuter arrives at a train station every morning between 6: 45 am - 7: 05 am (you may assume the arrival time is uniformly distributed). Trains leave the station at 6: 48 am, 6.55 am, and 7: 03 am. Find the probability that the commuter will have to wait nor more than 4 minutes for a train to leave.

Explanation / Answer

Answer to question# 3)

Part a)

We got the rate as 3 per hour

this means for 2 hours the rate would be 6 per 2 hours

we need to find the probability that no call arrives in first two hours, this means x = 0

The arrival rate follows poisson distribution with lambda = 6

P(x=0) = e^-8 * (8)^0 /0!

P(x=0) = e^-8 * 1 /1

P(x=0) = 0.000335

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