The Consumer Financial Protection Bureau’s consumer response team hears directly from consumers about the challenges they face in the marketplace, brings their concerns to the attention of financial institutions, and assists in addressing their complaints. Consumer response accepts complaints related to mortgages, bank accounts and services, private student loans, other consumer loans, and credit reporting. Of the consumers who registered a bank account and service complaint, 45% cited “account management” as the type of complaint; these complaints are related to opening, closing, or managing the account and address issues, such as confusing marketing, denial, fees, statements, and joint accounts. (Source: Consumer Response Annual Report, 1.usa.gov/1kjpS2k)

Consider a sample of 20 consumers who registered bank account and service complaints. Use the binomial model to answer the following questions:

1. What is the expected value, or mean of the binomial distribution?

2. What is the standard deviation of the binomial distribution?

3. What is the probability that 10 of the 20 consumers cited “account management” as the type of complaint?

4. What is the probability that no more than 5 of the consumers cited “account management” as the type of complaint?

5. What is the probability that 5 or more of the consumers cited “account management” as the type of complaint?