A graphing calculator may be used wherever possible. However, you need to substantiate your answers for full credit. If necessary, you can round your answers to four decimal places. If you run out of room for your response, use the back of the page [1](16) The paper "Caffeine Knowledge, Attitudes, and Consumption in Adult Women" (. of Nutrition Edu. (1992): 179-184) reported the following summary data on daily caffeine consumption for a sample of 49 adult women. n =49, X =215 mg, $ = 235 mg, range: 5 to 1176 a) Does it appear plausible that the population distribution of daily caffeine consumption is normal? Explain. b) Is it necessary to assume a normal population distribution to estimate or test hypotheses about the value of the population mean consumption? Explain. c) Use the sample data to construct a 95% confidence interval estimate for the value of the popula- tion mean consumption. d) Suppose it had previously been believed that the mean consumption was at most 200 mg. Does the given data contradict this prior belief using the result in (c)