Question

1. The time between calls to a corporate office is exponentially distributed with a mean of 10 minutes. (a) What is the probability that there are more than three calls in one-half hour? (b) What is the probability that there are no calls within one half hour? (c) Determine x such that the probability that there are no calls within x hours is 0.01

Answer 1

a)expected number of call in half hour =30/10 =3

P(more than 3 calls in half hour)=P(X>3) =1-P(X<=3) =1-(e^-3*3⁰/0!+e^-3*3¹/1!+e^-3*3²/2!+e^-3*3³/3!) =0.3528

b)

P(no call) =P(X=0)=e^-3*3⁰/0! =0.0498

c)

P(no call in x hours )=e^-6x =0.01

taking log and solving"

x =-ln(0.01)/6 =0.7675 Hours