Q2(a) A fertilizer mixing machine is set to give 12 kg of nitrate for every quintal [15] bag of fertilizer. Six bags are examined and the percentages of nitrate are recorded as: 11, 14, 13, 12, 13, 14 (1) Is there any reason to believe that the machine is defective at 5% level of significance? (ii) Find the 95% confidence interval for the population mean. (b) Each sample of water has a 10% chance of containing a particular [10] organic pollutant. Assume that the samples are independent with regard to the presence of the pollutant. Find the probability that in the next 18 samples, (i) none contains the pollutant. (i/) at least 4 contain the pollutant. Total 25 Marks Page 2 of 6 Section B (Answer any TWO Full Questions) Q3(a) The continuous random variable has a probability density function given [13] by : 02.5). (ili) Find E(X) and V(X)