b) Let the number of days when a certain train service is broken in 3 years (1 year is 365 days) be 1 time. (Hint: you may use Poisson's distribution to approximate the Binomial distribution) The Poisson's probability distribution is given by: P(x) - He - with u being x! the average of the variable x. i. What is the probability that the same train service is broken less than 3 times in 5,000 days? ii. What is the probability that the same train service is broken more than 10 times in 10,000 days? (8 marks) C) A certain chip manufacturer produces memory chips with a mean current consumption of 100mA and standard deviation of the current consumption is 5mA. Assume that the chip current consumption follows a normal distribution. We also assume that the resolution of the current measurement is 1mA (smallest difference between chips is 1mA). A standardized normal distribution table is provided at the Appendix of this paper. i. What percentage of the chips will have current consumption that is equal to or larger than 106mA? ii. What percentage of the chips will have current consumption that is between 95mA and 105mA? (8 marks)Question 6. a) A box has 100 balls consisting of 30 red colour balls and 70 green colour balls. On top of that, there are two types of weight for the balls, 1 kg and 2 kg, as shown in the table below. A ball is now picked randomly from the box. Red Green Total 1 kg 20 20 40 2 kg 10 50 60 Total 30 70 100 Calculate: i. Probability of picking a green ball ii. Probability of picking a red ball that is 2 kg. (4 marks)