QUESTION 4 (25 marks) (a) The scores of 800 candidates in an examination are normally distributed with a mean of 65 marks and a standard deviation of 20 marks. (i) Find the probability that a candidate selected at random obtains marks between 60 and 80. (4 marks) (ii) If 8.85% of the candidates obtained a distinction by scoring X marks or more, find X. (4 marks) (b) Suppose that Y has density function f(v)= ky(1-y) , forOsys1 0 , elsewhere (i) Find the value of k that makes f(y) a probability density function. (5 marks) (ii) Find P(Y