You may need to use the appropriate appendix table or technology to answer this question.

A random sample of 121 checking accounts at a bank showed an average daily balance of $285. The standard deviation of the population is known to be $55.

(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. Choose a answer below

-Yes, the sample is large and the standard deviation of the population is known so we also need to know that the shape of the distribution is at least approximately bell shaped.

-No, the sample is large and the standard deviation of the population is known so we do not need to know anything about the shape of the distribution.

-No, the standard deviation is larger than the mean so we do not need to know anything about the shape of the distribution.

-No, the mean is larger than the standard deviation so we do not need to know anything about the shape of the distribution.

-Yes, the mean is larger than the standard deviation so we also need to know that the shape of the distribution is at least approximately bell shaped.

(b)Find the standard error of the mean (in dollars).$

(c)Give a point estimate of the population mean (in dollars).$

(d)Construct an 80% confidence interval for the population mean (in dollars). (Round your answers to the nearest cent.)$ to $

(e)Construct a 95% confidence interval for the population mean (in dollars). (Round your answers to the nearest cent.)$ to $