Lake Edge Wood Ltd. is a small Ontario business that specializes in design, manufacturing and selling of unique wooden products. Some of the company's top products include boards, boxes and coasters. As a part of the annual budgeting process, the managerial accountant selected a random sample of 56 batches of boards and determined that the manufacturing overhead per batch is $324 with a sample standard deviation of $82. The population standard deviation of the manufacturing overhead per batch is known to be $85.

(a) What can you conclude about the shape of the distribution? Why? (2 marks)

(b) Construct a 78% confidence interval for the population mean amount of the manufacturing overhead per batch. (3 marks)

(c) Construct a 72% confidence interval for the population mean amount of the manufacturing overhead per batch. (3 marks)

(d) Review your results in part (b) and part (c). Which of these has the smaller confidence interval and why? (1 mark)

(e) Interpret the interval in part (c). (1 mark)