The diameter of a rivet (in mm) is a random variable with probability density functionS 6(x – 12) (13 – x) f(x) = 0 {ov 12 < x < 13 otherwise a. What is the probability that the diameter is less than 12. 5 mm? b. Find the mean diameter. c. Find the standard deviation of the diameters. d. Find the cumulative distribution function of the diameter. e. The specification for the diameter is 12. 3 to 12. 7 mm. What is the probability that the speci- fication is met?