Motel Reservations. M. Driscoll and N. Weiss discussed the modeling and solution of problems concerning motel reservation networks in “An Application of Queuing Theory to Reservation Networks” (TIMS, Vol. 22, No. 5, pp. 540–546). They defined a Type 1 call to be a call from a motel’s computer terminal to the national reservation center. For a certain motel, the number, X, of Type 1 calls per hour has a Poisson distribution with parameter λ = 1.7. Determine the probability that the number of Type 1 calls made from this motel during a period of 1 hour will be

a. exactly one.

b. at most two.

c. at least two. (Hint: Use the complementation rule.)

d. Find and interpret the mean of the random variable X.

e. Determine the standard deviation of X.