Recall in Exercise 5.34 (page 222) 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 μx, σ2x, and σx.
e. Find the probability that the time between arrivals falls within one standard deviation of the mean; within two standard deviations of the mean.