quantitative studies

Question 2: [25 marks] (a) Itis known that 70% of the students staying less than 20 km away from the campus. 80% of them using public transport to travel to the campus. Of those who are staying more than 20 km away from the campus, 10% of them using public transport to travel to the campus. (1) Draw a well-labelled probability tree diagram with the joint probabilities calculated to illustrate this situation. (5 marks) (11) Find the probability that a randomly selected student using public transport to travel to campus. (2 marks) (111) Find the probability that a randomly selected student staying less than 20 km away from the campus given that he/she does not use public transport to travel to campus. (3 marks) (iv) Are the events \"staying less than 20 km away from the campus and *\"using public transport to travel to campus independent? Explain. (3 marks) (b) In TAR UMT, 40% of the students having classes on Saturday. If 6 students are selected at random, find the probability that (i) at least 5 students having classes on Saturday. (3 marks) (11) at most 2 students do not have classes on Saturday. (3 marks) (c) A factory finds that the average weight of a packet of flour packed by a certain machine is 500 g and standard deviation is 50 g. Assume that the weights are normally distributed. (1) Find the probability that a randomly selected packet of flour weight less than 400 g. (3 marks) (i) Find the value of k if 25% of the packets of flour weight less than k. 3 ma