The width of bolts of fabric is normally distributed with mean 950 mm (millimeters) ad standard deviation 10 mm.

(a) What is the probability that a randomly chosen bolt has a width of between 947 and 958 mm?

(b) Four bolts are randomly selected for testing. What is the probability that exactly two of the four bolts have has a widths between 947 and 958 mm?

(c) What assumptions did you make in part (b)?

(d) Find C such that a randomly chosen bolt has a width greater than C with probability 0.8531.