An auditor, examining a total of 820 accounts receivable of a corporation, took a random sample of 60 of them. The sample mean was $127.43, and the sample standard deviation 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 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 820 accounts.