The modeling and solution of problems concerning motel reservation networks for motels were studied. Researchers defined a Type I 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 =2.5. Complete parts (a) through (e) below.

a. Determine the probability that the number of Type 1 calls made from this motel during a period of 1 hour will be exactly one.

b. Determine the probability that the number of Type 1 calls made from this motel during a period of 1 hour will be at most two.

c. Determine the probability that the number of Type 1 calls made from this motel during a period of 1 hour will be at least two. (Hint: Use the complementation rule.)

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

e. Find the standard deviation of the random variable X.