(a). Suppose X has a Poisson distribution with parameter ?=11.44. Find the following.

(i). The mean of X.

(ii). The standard deviation of X.

(b). The number of lightning strikes in a year at the top of particular mountain has a poison distribution with parameter ?=2.9.Find the following.

(i). The probability that in a randomly selected year the number of striking is less than or equal to 5.

(ii). The probability that in a randomly selected year the number of striking is greater than 5.

(c). The probability that a call received by a certain switchboard will be a wrong number is 1 per 100 calls. Use poison approximation to the binomial distribution to find the probability that among 120 calls received by the switchboard,

(i). There is no wrong numbers.

(ii). There is exactly one wrong number.

(iii). There are exactly two wrong numbers.

(iv). There are exactly three wrong numbers.

(v). There are at most three wrong numbers.