Fibertec is Canada's leading high-performance, high energy efficient fiberglass windows and doors for the residential and commercial markets. The company has been operating for more than 25 years and is located just outside of Toronto. In March 2021, the company's operations manager was in the process of re-negotiating its contracts for raw materials. Based on the currently available information, the average order quantity of raw materials per purchase order is 394 kg. Suppose the standard deviation of order quantity is 25 kg per purchase order. Suppose that the operations manager took a random sample of 76 purchase orders from 2021.

(a)What can you conclude about the shape of the distribution of the sample mean? Why? (2 mark)

(b)Compute the standard error of the sample mean for the operations manager. (1 mark)

(c)What is the probability that the sample average of order quantity of raw materials would be between 390 and 402 kg per purchase order? (5 marks)

(d)What is the probability that the sample mean would be less than 410 kg? (3 marks)

(e)State one possible reason why the operations manager uses sampling. Explain your reasoning. (2 marks)