For a $10 monthly fee, a gas company guarantees customers complete service. Records show that of their 20,000 customers, 1000 customers required one service call in a typical month, and 200 required two service calls. No customer required more than two service calls. Each service call costs the gas company $80.

(a) Let X be the random variable defined as the profit (per

month) that the gas company makes on a randomly chosen

customer. Construct the probability distribution of X. [4

marks]

(b) Calculate the mean and standard deviation of X, and

interpret the values of these parameters. [4 marks]