6. (27 points) A ball bearing refers to a type of rolling-element bearing that uses balls to maintain the separation between the moving parts of the bearing. The diameters of ball bearings manufactured are given to be normally distributed with a mean of 5.5 mm and standard deviation of 0.80 mm. Answer the following questions below. a) Find the probability that a randomly selected ball bearing has a diameter less than 5.88 mm. b) Suppose that a random sample of 35 ball bearings are manufactured. Find the probability that these ball bearings have a mean diameter greater than 5.95 mm. c) If an order comes in for 25,000 ball bearings, how many bearings should the plant manager manufacture if the order states that all ball bearings must have a diameter 5.25 mm and 5.45 mm