Question: 8 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.

a. Determine a point estimate for the population mean budget, for such home improvement jobs. Interpret your answer in words. (Note: The sum of the data is $129,849.)

b. Obtain a 95.44% confidence interval for the population mean budget, 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 budget for such home improvements jobs be exactly normally distributed for the confidence interval that you obtained in part (b) to be approximately correct? Explain your answer.