Home Improvements. The American Express Retail Index provides information on budget amounts for home improvements.

The following table displays the budgets, in dollars, of 45 randomly sampled home improvement jobs in the United States.

3179 1032 1822 4093 2285 1478 955 2773 514 3915 4800 3843 5265 2467 2353 4200 3146 551 2659 4660 3570 1598 2605 3643 2816 3125 3104 4503 2911 3605 2948 1421 1910 5145 4557 2026 2750 2069 3056 2550 631 4550 5069 2124 1573

a. Determine a point estimate for the population mean budget, μ, for such home improvement jobs. Interpret your answer in words.

(Note: The sum of the data is $129,849.)

b. Obtain a 95% confidence interval for the population mean budget, μ, for such home improvement jobs and interpret your result in words. Assume that the population standard deviation of budgets for home improvement jobs is $1350.

c. How would you decide whether budgets for such home improvement jobs are approximately normally distributed?

d. Must the budgets for such home improvement jobs be exactly normally distributed for the confidence interval that you obtained in part

(b) to be approximately correct? Explain your answer.