An auditor, examining a total of 820 accounts receivable of a corporation, took a random sample of sixty of them. The sample mean was $127.43, and the sample standard devia- tion was $43.27.

(a) Using an unbiased estimation procedure, find an estimate of the population mean.

(b) Using an unbiased estimation procedure, find an estimate of the variance of the sam- ple mean.

(c) Find a 90% confidence interval for the population mean.

(d) A statistician found, for the population mean, a confidence interval running from $117.43 to $137.43. What is the probability content of this interval?