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Question 26 A recent consumer behaviour survey reports that 75% of all purchases at a supermarket in Launceston are made with a credit card. Let X be the number among 20 randomly selected purchases made with a credit card. a ) Determine the probability that 15 purchases are made with a credit card, e.g. find P(X=15). [7 marks] b) Determine the probability that at least half of the purchases are made with a credit card, e.g. find P(X$10). [7 marks] C) Determine the mean and variance of the purchases made with a credit card. Discuss your results. [2+2+2=6 marks] [Total marks for Question 26 - 20 marks]