The tuition fees for various levels of study at a tuition centre follows a normal distribution with a moan of RM1850 and a standard deviation of RM230. What percentage of the tuition fee is below RM7507 (4 marks) Given that 80's of the students' tuition fees are more than RM A. find the value of A. (3 marks) [Toil :34 marks]Q2. (a) A student goes to class by bus, car or motorbike. The probability he travels by these mode of transports are equally likely. The probability that he will be late for class if he goes by bus, car and motorbike are 2 1 9' 10 - and respectively. 15 Draw a well-labelled probability tree diagram with the joint probabilities calculated to illustrate the situation. (5 marks) Find the probability that on a randomly selected day, he is not late to class. (2 marks) (iii) What is the probability that he goes to class by motorbike if he is late for class on a particular day? (3 marks) (iv) Are the events "lore to class" and "goes to class by car" independent? Explain your answer. (2 marks) (b) A survey showed that 0.9% of the students choose to have online class instead of physical class. (i) Calculate the probability that, in a random sample of 10 students, at least 9 students will choose to have physical class. (4 marks) (ii) Determine the probability that, in a random sample of 200 students, less than 3 students will choose to have online class. (4 marks) (9) The number of new students joining the tuition class follow a Poisson distribution with a mean of 2 per week. Calculate the probability that more than 2 new students joining the tuition class in 2 weeks; (3.5 marks) at least I new student joining the tuition class in 2 days. (3.5 marks)