solve all parts

2. You change jobs to the company Mars-Hed-Hot-Sauce that produce hot sauce from chili peppers. The hotness in chili peppers are measured in SHU (Scoviile Heat Units). Since individual chili peppers vary in humans, the sauce will also vary in hotness from batch to batch. The plant has two cookers that produce hot sauce in batches with the hotness H. and H3. which we model as independent and identically distributed Gaussian random variables with mean 5000 SHU and standard deviation 300 SHU. The sauce from the cookers are fed into two bottling machines. The rst machine is fed with a mixture of 80% sauce From Cooker l and 20% sauce from Cooker 2. In a similar Fashion, the second machine use is fed with a mixture of 20% sauce from Cooker l and 80% from Cooker 2. (a) What is the distribution for the hotness in bottles from Machine 2? Motivate. (2p) (1:) What is the expected value and standard deviation of the hotness. in a bottle from Machine 2? (41)) [c] Suppose the hotness in the bottles from bottling Machine 1 is measured to be 5100 SHU. What is the best estimate (in the MSE sense) of the hotness in the bottles from Machine 2? (4p) (:1) The bottles from Machine 2 will be sold in the US. The company runs the rial-t of being sued if the hotness in the bottles exceed 5500 SHU. Given the same measurement as in Part (c). what it the probability of the hotness in the bottles exceed 5500 SHU? (4p)