1. [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