A company markets its line of products directly to consumers through telephone solicitation. Salespersons are given a base pay that depends on the number of documented phone calls made plus incentive pay for each phone call that results in a sale. It can be assumed that the number of phone calls that result in sale is a binomial random variable with parameters \(p\) (probability of sale) and \(n\) (number of phone calls). The base pay is \(\$ .50\) per call and the incentive pay is \(\$ 5.00\) per sale.

(a) Derive the probability distribution of pay received by a salesperson making \(\mathrm{n}\) calls in a day.

(b) Given that 100 calls are made in a day and \(p=.05\), what is the expected pay of the salesperson? What is the probability that pay will be \(\$ 50\) or less?