As any credit-granting agency knows, there are always some customers who default on credit charges. Typically, customers are grouped into relatively homogeneous categories, so that customers within any category have approximately the same chance of defaulting on their credit charges. Here we will look at one particular group of customers. We assume each of these customers has (1) probability 0.07 of defaulting on his or her current credit charges, and (2) total credit charges that are normally distributed with mean $350 and standard deviation $100. We also assume that if a customer defaults, 20% of his or her charges can be recovered. The other 80% are written off as bad debt.
a. What is the probability that a typical customer in this group will default and produce a write-off of more than $250 in bad debt?
b. If there are 500 customers in this group, what are the mean and standard deviation of the number of customers who will meet the description in part a?
c. Again assuming there are 500 customers in this group, what is the probability that at least 25 of them will meet the description in part a?
d. Suppose now that nothing is recovered from a default—the whole amount is written off as bad debt. Show how to simulate the total amount of bad debt from 500 customers in just two cells, one with a binomial calculation, the other with a normal calculation.