A senior loan officer for Whitney National Bank has recently studied the bank’s real estate loan portfolio and found that the distribution of loan balances is 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 concerned that the sample selected by the auditors is not representative of the overall portfolio. In particular, he 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.