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