A salesperson who sells an appliance to small businesses calls on 4 potential buyers every day. Based on historical information, the probability of making a sale is 12% for every potential buyer. Potential buyers’ decisions are assumed to be independent. Let the random variable X be the total count of successful sales that the salesperson makes on a given day.

a. What is the probability that the salesperson fails to make any sales on a given day? 

b. What is the probability that the salesperson makes multiple sales (more than one) on a given day? 

c. If the selling price of the appliance is $999, what is the probability that the revenue from the salesperson’s sales exceeds $1000 on a given day? 

d. Calculate the expected number and standard deviation of successful sales on a given day. 

e. Assuming again that the selling price of the appliance is $999, what is the expected revenue from the salesperson’s sales for a 5-day workweek?