a)A machine is used to produce a number of loaves that follow a Poisson distribution. The probability that the machine will produce 3 loaves is 0.2158. The probability of producing 5 loaves is 0.1322. Calculate the probability of the machine producing 4 loaves. (3 marks)

b)The probability of getting a defective match stick from a factory is 0.004. A box contains 100 match sticks. From 1,000 boxes how many boxes will contain 4 defective match sticks. (use Poisson approximation to binomial distribution)(3 marks)

c)The probability of finding a defective fuse in a factory is 0.04. A sample of 9 fuses were selected. Find the probability of finding more than 2 defective fuses.(2 marks)

d)A candidate was supported by 350 people in a district with 400 people. In another district with 500 people the support was 475 people. Test if there is a difference between the two districts.(5 marks)