(b) Suppose customers arrive in a store according to a Poisson process of rate λ = 8 customers per hour. The store opens at 8 am. (i) Find the probability of observing at most 2 customers arriving at the store during a 15-minute interval. (5 marks) (ii) Find the probability that 12 customers arrive before 10 am and there is a total of 16 arrivals by 11 am. (7 marks) (iii) Find the probability that the inter-arrival time of customers is less than 1 minute. (6 marks)
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(i) We know that the Poisson process has a rate of 8 customers per hour, which means that the average number of customers arriving in a 15-minute interval is 2. Show more…
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