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

The Consumer Financial Protection Bureaus consumer response team hears directly

from consumers about the challenges they face in the marketplace, brings their concerns

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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, 41% cited ”account

management” as the type of complaint; these complaints are related to opening, closing,

or managing the account and addressing issues, such as confusing marketing, denial,

fees, statements, and joint accounts. Consider a sample of 20 consumers who registered

bank accounts and service complaints. Use the binomial model to answer the following

questions:

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?