Historical Data Collected at the Commonwealth Bank in Sydney Revealed

question 45

Essay

Historical data collected at the Commonwealth Bank in Sydney revealed that 80% of all customers applying for a loan are accepted. Suppose that 50 new loan applications are selected at random.
a. Find the expected value and the standard deviation of the number of loans that will be accepted by the bank.
b. What is the probability that at least 42 loans will be accepted?
c. What is the probability that the number of loans rejected is between 10 and 15, inclusive?

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Definitions:

Deadweight Loss

The loss of economic efficiency that occurs when the equilibrium for a good or a service is not achieved, leading to a misallocation of resources.

Demand Curve

A graphical representation showing the relationship between the price of a good or service and the quantity demanded by consumers at various price levels.

Consumer Surplus

The divergence between the aggregate amount consumers are willing and have the means to pay for a good or service, and what they truly pay.

Producer Surplus

The disparity between what sellers are ready to take for a product or service and the actual amount they get.