A recent consumer behavior 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(X10).

[7 marks]

c)Determine the mean and variance of the purchases made with a credit card. Discuss your results.

[2+2+2=6 marks]