Question 2 (a) Dr. Tan has taught BUS105 many years, and he knows that around 75% of students will read the study guide. Among those who read the study guide, 87% will pass the course. Among students who did not read the study guide, 65% will pass the course. (i) Identify the probability that a student will pass BUS105. (5 marks) (ii) Raymond took BUS105 last semester, and he passed BUS105. What is the probability that he had read the study guide? (7 marks) (b) Statistics show that the distribution of monthly rent for a 4-room HDB flat has a mcan of $2,530 and a standard deviation of $240. Assume that the distribution of monthly rent for a 4-room HDB flat follows a normal distribution, what is the probability of renting a flat at a price cheaper than $2,000? (5 marks) (ii) In fact, the distribution of monthly rent for a 4-room HDB flat is positively skewed. What is the probability of finding the mean rent of a sample of 35 units of 4-room HDB flat more than $2,6007 (8 marks)