Telephone calls to the national reservation center for motels were studied. A certain model 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 λ=1.8. Answer the following questions.

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

four. (Hint: Use the complementation​ rule.)

d. Find the mean of the random variable X.

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