A local coffee shop records the amount of coffee beans, in kilograms, used each week. Assume the weekly coffee bean usage can be modelled using a normal probability distribution with a mean of 184 kg and a standard deviation of 47 kg. Let X represent the usage for a randomly chosen week. (a) In what proportion of all weeks will the coffee shop use between 165 kg and 240 kg of coffee beans? (b) How many kilograms of coffee beans should the coffee shop have on hand to have only a 1% chance of running out of coffee beans? (c) The coffee shop manager plans to select a random sample of 36 weeks and measures the demand in each week. What is the sampling distribution of the sample mean X ? Explain. (d) What is the probability that in a sample of 36 randomly chosen weeks, the average weekly usage will not exceed 200 kg? (e) Suppose that the weekly coffee bean usage does not follow a normal distribution. Would your answer in part (d) still be correct? Explain.