. (15 points) The Rockwell hardness of certain metal pins is known to have a mean µ = 50 and a standard deviation σ = 4. (a) (5 points) Assume that the distribution of all such pin hardness measurements is known to be normal. If we randomly select 1 pin from the population, what is the probability that the hardness is less than 46? (b) (5 points) Assume that the distribution of all such pin hardness measurements is known to be normal. If now a random sample of 16 pins is obtained, what is the probability that the average hardness is less than 46? (c) (5 points) Assume that the distribution of all such pin hardness measurements is known to be not normal. If now a random sample of 64 pins is obtained, what is the probability that the average hardness is less than 46?