Question

The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 11 seconds.

(a) Sketch this exponential probability distribution.

(b) What is the probability that the arrival time between vehicles is 11 seconds or less?

(c) What is the probability that the arrival time between vehicles is 7 seconds or less?

(d) What is the probability of 33 or more seconds between vehicle arrivals?

Answer 1

a)

b)

Here parameter β =

11.000

F(x)=P(X<x)=(1/β)e-x/β

probability =

P(X<11)=

1-exp(-11/11)=

0.6321

c)

probability =

P(X<7)=

1-exp(-7/11)=

0.4708

d)

probability =

P(X>33)=

1-P(X<33)=

1-(1-exp(-33/11))=

0.0498