A senior loan officer for Whitney National Bank has recently studied the bank’s real estate loan portfolio and found that the loan balances are approximately normally distributed with a mean of $155,600 and a standard deviation equal to $33,050. As part of an internal audit, bank auditors recently randomly selected 100 real estate loans from the portfolio of all loans and found that 80 of these loans had balances below $170,000. The senior loan officer is interested in knowing the expected proportion of loans in the portfolio that would have balances below $170,000.

You are asked to conduct an appropriate analysis and write a short report to the senior loan officers with your conclusion about the sample.