Question 2 (a) Mrs Reena has regularly contacted three companies (A, B and C) for her quarterly servicing of aircons. If A services her aircons, the probability that there will be no problem with the aircons in the next quarter is 0.8. The same probability for B is 0.7 and for C is 0.6. If all her aircons do not show any problems, she will engage the same company in the next quarter. If any of the aircons shows a problem, then she will engage A with a probability of 0.5, B with a probability of 0.3 or C with a probability of 0.2 in the next quarter. One of her aircons had a problem last quarter. (i) Identify the probability that her aircons will have no problem in the next quarter. (ii) Given that her aircons had no problem in the next quarter, what is the probability that she engaged C? (iii) What is the probability that she will engage A for the next two quarters? (12 marks) (b) A study showed that the length of human pregnancies is normally distributed with mean 266 days and standard deviation 16 days. (i) (ii) If a pregnant woman is randomly selected, identify the probability that her length of pregnancy is between 260 and 270 days. If twenty (20) women are randomly selected, report the probability that the mean length of pregnancies is greater than 265 days. (13 marks)