l. [32 pts total] A researcher proposes to model daily coffee consumption among OSU students by a normal distribution with mean 20 oz and standard deviation 4 oz. (a) [4 pts] Comment on whether such a model is appropriate for coffee comsumption at OSU. Points will be assigned for making valid arguments for/against the model. (b) [4 pts] One OSU student was found to be consuming 32 oz of coffee a day. To investigate if this is excessive consumption, compute the probability that a randomly selected student will consume more than 32 oz of coffee. (c) [4 pts] What is the probability that a randomly selected student will have coffee consumption in the range [14, 26] oz.'? (d) [5 pts] What is the probability that a randomly selected student will have coffee consumption in the range [mean-SD, mean+SD]? (e) [5 pts] Find the amount of coffee consumption that only 5% of the students will exceed? (f) [10 pts] Verify your answers for parts (b) through (d) using Monte-Carlo simulations in R by performing the following steps: ' Generate 1 million random samples from the normal distribution with appropriate mean and SD. ' Compute the Monte-Carlo estimates of the required probabilities in parts (b), (c) and (d). ' Comment on their similarity with your theoretical calculations above. 1" Mr A A A 111' j 'I I 1 AI A .f'A' f' I' I I I l 1\" I'I'VI