This question is worth 16 points, with option a being 12 points and option b being 4 points. Solve this question on a white paper and email your solutions. Use 4 digits in decimal parts after all calculations are done. Just submit the answer of option a to the LMS. A chemical company produces bags of fertilizer. Manager claims that they fill each bag with at least 50.2 kilograms of fertilizer. Assume that the standard deviation for the amount in each bag is 1.2 kilograms, The decision rule is adopted to shut down the filling machine if the sample mean weight for a sample of 40 bags is below 49.8, Suppose that the true mean weight of bags is 50 kilograms. a) Using this decision rule, what is the probability of not rejecting false null hypothesis? b) Find the probability of rejecting false null hypothesis. 0.01 0.02 0:03 0.04 0.06 0.06 0.07 +0 50000 50399 50798 51197 51545 53983