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Question 6 [20 marks]: A Tasmanian distillery has imported a new machine that is used to ll bottles of whisky. However, the machine cannot ll exactly the same amount of whisky into every,r bottle. After one month, it is observed that the quantity poured into a 1 litre bottle is nonatty distributed with a mean of 1.02 litres and a standard deviation of Ill litres. (a) 1'What is the probability of a bottle of whisky containing less than 0.95 litres? [I 0 marks] (b) Suppose the new machine can be adjusted to any mean while leaving the standard deviation unchanged. To what mean should we set the machine so that only 1% of bottles contain less than 1 litre? [I 0 marks}