College debt (2.2) A report published by the Federal Reserve Bank of New York in 2012 reported the results of a nationwide study of college student debt.

Researchers found that the average student loan balance per borrower is $23,300. They also reported that about one-quarter of borrowers owe more than

$28,000.14

(a) Assuming that the distribution of student loan balances is approximately Normal, estimate the standard deviation of the distribution of student loan balances.

(b) Assuming that the distribution of student loan balances is approximately Normal, use your answer to part

(a) to estimate the proportion of borrowers who owe more than

$54,000.

(c) In fact, the report states that about 10% of borrowers owe more than $54,000. What does this fact indicate about the shape of the distribution of student loan balances?

(d) The report also states that the median student loan balance is $12,800. Does this fact support your conclusion in part (c)? Explain.