8. 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 358 Chapter 6 Sampling, Sample Moments, Sampling Distributions, andSimulation the number of phone calls that result in sales is a binomial random variable with parameters p (probability of sale) and n (number of phone calls). The base pay is

$0.50 per call, and the incentive pay is $5.00 per sale.

a. Derive the probability distribution of pay received by a salesperson making 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 the pay will be $50 or less?

9. The daily quantity of a commodity that can be produced using a certain type of production technology is given by the outcome of the random variable Q, defined as Q = lOxi3s XiS V,