4) A recent consumer behaviour survey reports that \65 of all purchases at a supermarket in Launceston are made with a credit card. Let \\( \\mathrm{X} \\) be the number among 10 randomly selected purchases made with a credit card. a) Determine the probability that 5 purchases are made with a credit card, e.g. find \\( P(X=5) \\). b) Determine the probability that at least half of the purchases are made with a credit card, e.g. find \\( P(X \\geq 5) \\). c) Determine the mean and variance of the purchases made with a credit card. Discuss your results