(4) A large loan company specializes in making automobile loans for used cars. The board of directors wants to estimate the average amount loaned for used cars during the last year. The company takes a simple random sample of 150 customers for this period. The mean amount loaned for this sample of 150 loans is x= $8500 and the sample standard deviation is s = $1100. (*) (a) Find a 95% confidence interval for population mean . [Round to the nearest cent] (b) For a day in which 12 loans are made, use the result from part (a) to estimate the rang of dollar values for the total amount of money loaned. [Round to the nearest cent] (c) How large a sample should the loan company have used to be 95% confident that they are within $100 of the true population mean? [Assume the sample standard deviation is the same as the population standard deviation commonly found in that industry.] (5) Louis is a waiter at a famous gourmet deli in New York City. The Internal Revenue Service is doing an audit of his tax return. In particular, the IRS wants to know the average amount Louis receives for a tip. In an effort to satisfy the IRS, Louis took a random sample of 6 credit card receipts, each of which indicated his tip. The tip results were: $10.50 $8.75 $16.56 $12.65 $16.10 $7.50 (a) Compute the sample mean x and sample standard deviation for his tips. [2 each] [Use your calculator & round to the nearest cent] x= _ and s= (*) (b) Find a 90% confidence interval for the population mean of tip amounts.