Question 3 (a) In the long run 40% of patients treated for a particular disease with the drug Ivermectin are qured. If a doctor were to treat 10 randomly chosen patients with the drug, without using * Binomial table, (i) find the probability that exactly 7 are cured. (2 marks) (ii) find the probability that less than 2 are cured. (3 marks) (iii) find the probability that 6 are not cured. (3 marks) (iv) calculate the mean and variance of the number of cures in this group of 10 patients. (2 marks) (b) The following table gives the probability distribution of the number of books purchased per hit by Amazon.com shoppers. Number of books 0 2 3 4 5 Probability 0.35 0.2 0.2 0. 1 0.1 0.05 (i) Find the probability of an Amazon. com visitor buying more than 3 books per hit. (1 mark) (ii) Find the mean and variance of the number of books purchased per hit. (5 marks) (C) The number of accidents occurred in a highway each week is Poisson distributed with a mean of 5.2. Without using a Poisson table, find the probability that there are more than one accidents occurred in 2 weeks. (4 marks)