A foreclosure is a legal process that a lender uses to recover the balance of a mortgage owed by a homeowner who has stopped making payments. An unusually high volume of foreclosures occurred during the most recent recession, and as a result, errors were made in the foreclosure process to a significant number of borrowers. For example, auditors found that 24% of foreclosures processed by PNC Financial Services had errors that would have required compensation for the borrowers. A random sample of five foreclosures was selected from PNC Financial Services.

a. What is the probability that exactly three foreclosures from this sample will have an error that would have required compensation?

b. What is the probability that none of the foreclosures from this sample will have an error that would have required compensation?

c. What is the probability that two or fewer foreclosures from this sample will have an error that would have required compensation?

d. Construct a histogram for this distribution.