Recall in Exercise 5.32 (page 212) that the number of customer arrivals at a bank's drive-up window in a 15-minute period is Poisson distributed with a mean of seven customer arrivals per 15-minute period. Define the random variable x to be the time (in minutes) between successive customer arrivals at the bank's drive-up window.
a Write the formula for the exponential probability curve of x.
b Sketch the probability curve of x.
c Find the probability that the time between arrivals is:
(1) Between one and two minutes.
(2) Less than one minute.
(3) More than three minutes.
(4) Between 1/2 and 31/2 minutes.
d Calculate mx, sx , and sx.
e Find the probability that the time between arrivals falls within one standard deviation of the mean; within two standard deviations of the mean.