Problem 3 (1 point each): A machine operation produces bearings Whose diameters are normally distributed with a = 4.2 mm and a = 0.08 mm. Use R to nd probabilities and quantiles, as appropriate. For any problems where you use R, be sure to include the code and R output. Summarize each answer in a sentence in the context of the problem. a) If you randomly select one bearing from this population, what is the probability that the bearing has a diameter less than 4 mm? b) What bearing diameter separates the largest 6% of diameters from among all diameters from this population? c) A randomly selected bearing from this group has a diameter of 4.25 mm. What percentile does this correspond to? d) A random sample of 20 bearings are selected from this population. What is the probability distribution for the sample mean diameter? Be sure to name the distribution and the values of any parameters. e) What is the probability that the mean bearing diameter exceeds 4.26 mm? 1) Find the probability that a random sample of 20 bearings has a mean diameter of exactly 4.2 mm