An auditor, examining a total of 830 accounts receivable of a corporation, took a random sample of 80 of them. The sample mean was €129.19, and the sample standard deviation was €43.11.

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 sample 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?

e. Find a 95% confidence interval for the total amount of these 830 accounts.