Question

Suppose the number of passengers arriving at an airline help desk follows a Poisson distribution. Passengers arrive at the desk on average every 10 minutes. Answer the following: Enter your final answers in the boxes below. Show ALL working by uploading your handwritten working for this question to Laulima Dropbox within 15 minutes of completing your exam. Correct answers without working shown will not receive full credit. Note that writing Excel functions does NOT qualify as showing working. a) (2) The probability that the next passenger arrives at the desk in more than a quarter of an hour. b) (3) The probability that the next passenger arrives at the help desk between a third of an hour and two-thirds of an hour. Show all work

Answer 1

here for exponential distribution parameter β = 10 minutes

F(x)=P(X<x)=1-e-x/β

a)

probability that the next passenger arrives at the desk in more than a quarter of an hour(15 minutes):

P(X>15)=1-P(X<15)=1-(1-e(-15/10))=e(-3/2))=

0.2231

b)

The probability that the next passenger arrives at the help desk between a third of an hour (20 minutes) and two-thirds of an hour(40 minutes):

P(20<X<40)=(1-e(-40/10))-(1-e(-20/10))=0.9817-0.8647 =

0.1170