Question

Problem 7 Customers shopping at Sprouts Store are both from east and west of Norman. The ones from the east of Norman arrive at the rate of 5 per minute. The ones from the west of Norman arrive at the rate of 7 per minute. Arrivals are random. Determine the probability that the interarrival time for all customers is less than 5 seconds?

Answer 1

here as number of custoer from east and west follows poisson distribution;

therefore total number of customers in 5 seconds also follow poisson distribution

with parameter expected number of customers in 5 seconds $\lambda$ =(5*5/60+7*5/60)=1 customer

hence P(interarrival time is less then 5 seconds)=1-P(no customer in 5 second)=1-(e^-1*1⁰/0!)=0.6321