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 ca in a typical month, and 200 required two service calls. No customer required more than two service calls. Each servic call costs the gas company $80. (a) Let X be the random variable dened as the prot (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]