please give step by step answers

Steel rods are manufactured with some variation in their diameters. The probability density function [pdf} of the diameter of a randondy selected rod is given by the following [in mm]: _ o [3f32)(:r 100?, as e: :s c: 102 g) F. {i}, otherwise. {a} 'What value ofa is required to make this a pdf? [3 marks] {b} Determine the cumulative distribution function for the diameters of randomly selected steel rods. [4 marks] (c) What is the expected value of this distribution? [3 marks] {(1} What is the variance and standard deviation of this distribution? [4 marks] [e] 'What is the probability that a randomly selected rod has a diameter between 100 and 1131 mm? [2 marks} (f) In a set of 5 randomly and independently selected rods, what is the probability that exactly two of them are between 100 and 101 mm in diameter? [3 marks]