Just let the variable be 4 as example, because I just want to know how to do :(

(a) Assume that the random variable Y follows a normal distribution N (,u,a + 1). Assume a is the last digital number of your student id number (for example, if your student number is 20987654D, then a = 4). [5 marks] (i) Write down your student number and variance 02 of this normal distribution; (ii) If the probability that the quadratic equation 1:2 + 833 + Y = 0 has no real root is 0.6664, nd the value of ii; (iii) Furthermore, nd the probability that the equation has exactly one solution. (b) Assume that the score of one standard test follows a normal distribution with ,u = 73 and or = 4. If all candidates are formed into many different groups of 36 individuals, will a group with average mark 85 be in the top ten percent of all groups with highest group average marks? [5 marks] (c) It is known that a machine produces defects at a probability of 5%. Find the probability that more than 40 defects are produced out of 500 items produced by this machine. [5 marks] ((1) An unfair die has four faces numbered 0, 1, 2, 3, and the probability of getting the corresponding score is shown in the following table face (score) 0 1 2 3 probability 0.1 0.2 0.3 0.4| Assume this die is rolled 90 times. Determine the probability that the sum of the 90 scores obtained will exceed 200. [5 marks]