Question 13 a) The lengths of carrots can be assumed to follow a Normal distribution with mean 18 cm and standard deviation 2.5 cm. A supermarket will accept carrots with lengths between 14 cm and 22 cm. What percentage of carrots will not be accepted by the supermarket? [4] b) In a large college, 20% of students are aged over 18. A group of 30 students is chosen at random. Find the probability between 5 and 8 students inclusive are aged over 18. [2] C) A discrete random variable, X, has probability function P(X = x) = kx for x = 1, 2, 3, 4, 5. i) Show that k = [1] ii) Find E(X). [2] You are given E(X2) = 15. iii) Find Var(X). [1] Another random variable, Y, is connected to X by the formula Y = 6X - 5. iv) Write down E(Y) and Var(Y). [2]