A random sample of 121 checking accounts at a bank showed an average daily balance of $289. The standard deviation of the population is known to be $66. A) Is it necessary to know anything about the...

A random sample of 121 checking accounts at a bank showed an average daily balance of $289. The standard deviation of the population is known to be $66.

A) Is it necessary to know anything about the shape of the distribution of the account balances in order to make an interval estimate of the mean of all the account balances? Explain.

The sample size is greater than 30 and population standard deviation is known so

AS PER-Central limit theorem we can assume the sampling distribution is NORMAL

So we don't need to assume Bell shape distribution

B) Find the standard deviation of the mean.

6

C) Give a point estimate of the population mean.

289

D) Construct an 80% confidence interval estimate for the mean.

E) Construct a 95% confidence interval for the mean.

F) Discuss why the answers in Parts D and E are different.