Question

Suppose that the amount of service(ordering a coffee and getting it done) time at a KU driving- through coffee shop is exponentially distributed with an expected value of 10 minutes. You arrive at the driving-through line while one customer is being served and one other customer is waiting in the line. The staff of the coffee shop informs you that the customer has already ordered a Cafe Latte and waited for 5 minutes. What is the probability that the customer will need no more than 5 minutes extra? What is the probability that you have to wait more than 15 minutes before you get your coffee?

Answer 1

Let t be the amount of tme taken by te coffea. shop to seye a cstome 1t ic -ven that t exp (io) Now, the tutomor hns ordered and alreadų waited ton 5 mnutui , hobab'ity that customo will nesd no more than bm extva the dersity function of eptove by 1-e 0,239チ 0 거。

0.606S Now, Probabiüity that you wil have to nit mo'ne than 15 min before gettingyou Coffea. > 5 〉 15) įg a subset of (t〉 5) No 1S 15 e0.2231 0.6065