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3. A milk company produces packs consisting of 4 bottles, each bottle nominally weighing 200 g. In practice, the actual weight of each bottle is normally distributed with mean 202 g and standard deviation 2.2 g. The weights are independent within and between packs. (a) What proportion of bottles weigh more than 200 g? [3 marks] (b) What proportion of packs weigh more than 800 g? [4 marks] (0) What is the probability that one or more bottles in a particular pack weigh more than 200 g? [4 marks] ((1) What is the approximate probability that at most 80 bottles out of a sample of 100 bottles weigh more than 200 g? [5 marks] (e) What should the standard deviation of the weight of bottles be if 99% of the packs are to weigh above 800 g while the mean weight of each bottle remains unchanged? [4 marks]