Question

Q4. Service time In a flight from Ottawa to London, there are two flight attendants: Caroline and Dylan. They work in two different sections of the Airbus A320. They work do not overlap. The airline expects its flight attendants to attend to passengers when they call for service in less than 1 minutes. Caroline on average answer 25% of the calls in less than a minute. Dylan on average answer 30 % of the call in less than a minute. If each of them serves 120 passengers in their section, answer the following questions: (Assume serving a passenger in less than a minute is a Bernoull trial; the probability of success remains the same in all trials. Not a very realistic assumption if the passengers start pressing the flight attendant bottom at the same time, but let's do it) What is the probability that Caroline serves at least 40 customers in less than a minute? Explain a. the method you use and the assumptions that should be satisfied. (5 points) b. What is the probability that Dylan serves at least 40 customers in less than a minute? Explain the method you use and the assumptions that should be satisfied. (5 points) c What is the probability that the number of passengers served by Dylan in less than a minute is smaller than the number of passengers served by Caroline in less than a minute? (5 points) A clear definition of random variable(s), choice of model, and a brief statement about the results have points

Answer 1

et Vaviebles Aenoting hether Ate Attend he i-t diiduul nxpeetively Reg nan mimte (as) Benmi (o'3) ,120 V , 120 indwiduals call cn A ttendant independentey 3crmoulli (0.25) ; 1,. 120 120 ; \ (avoline aftends i-th individual in css han a min ;1,^120 20 40 Shere 12D (120,0.25) 30 20-2 20i0.5) -1- 120-7 20 412 O. 025. 1; / Dy^an attendo j-th in dividual in less han a miin (4) we knpv that, Scanned with CamScanner CS >1,,120 O 0.40

Required robakility where 20 y2Bininl 120, 0) Į 20 0. 24 (Aw Ce) Required obakilitj 2D 2D (20 P Noio, here Xet uA asaume that, the nD. of pasacngers attendid by Caroline and bylan f Rnch Dther ave kecauae, they wvvk indipendent overAopping aectiond. theauired prolability in 2 different Therefove 2D- 20 20 Ex 0 120- 2o ハ201 120 0. 173 CS Scanned CamScanner (Ams)