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\"A sample of 20 cigarettes is tested to determine nicotine content and the average value observed w .2 mg. You may assume that the nicotine content of each cigarette is normally distributed. (a) Compute a 99 percent condence interval for the mean nicotine content of a cigarette if it is known that the standard deviation of a cigarette's nicotine content is a = 0.2 mg. (b) Suppose that the population variance is not known in advance of the experiment. If the sample standard deviation is 0.2 mg, compute a 99 percent condence interval for the mean nicotine content. (c) Following from part (b), give a 99 percent condence interval for the variance of the nicotine content. ((1) Do you think the calculations you have made in parts (a), (b) and (c) are correct if the nicotine content of each cigarette is not normally distributed? Explain your