Question

Do you dislike waiting in line? A supermarket chain has used computer simulation and information technology to reduce the average waiting time for customers at 2,300 stores. Using a new system, which allows the supermarket to better predict when shoppers will be checking out, the company was able to decrease average customer waiting time to just 19 seconds. (a) Assume that supermarket waiting times are exponentially distributed. Show the probability density function of waiting time at the supermarket. • X20 elsewhere (6) What is the probability that a customer will have to wait between 15 and 45 seconds? (Round your answer to four decimal places) 0.3605 1) What is the probability that a customer will have to wait more than 2 minutes? (Round your answer to four decimal places)

Answer 1

Solution Cliven data, Average Customer waiting time x = 19 seconds. a) Probability density farction of Walting time at the Supermarket P(X) = t.eo/ So fart.29, se so Lo otherwise. b) P(Customer will have to walt between 15 and us seconds) We know fox)= 1-e-ex Now PC152 x 245) - PCX205) - PCX215) - c-e-45/9) - Ci-e-18/19) 0.789 = (1-*2.366) – -6-0489) -(1-0.0937) -C1-0.4543) -0.9063 - 0.5457 => 0.3606 Seconds . P(Customer will walt blo 15 and us seconds) = 0.3606 seconds C) P(Customer will have to wait mse than 2 minutes): Hue 2 minutes = 120 seconds. ie P(x>120). p(>120) = 1-p(42120) l-a-e 10/19) -> 1-C1-e-63158) -> 1-1+0.0018 -0.0018 :. Plcustomer will have to wait moe than 2 mincetes) = 0.0018.