(a) From sales records of FDS Department Store, 25% of invoices are paid by cash, 35% are

paid with EPS and 40% are paid with a credit card. Twenty percent of the cash

purchases, 50% of the EPS purchases and 90% of the credit card purchases are for the

amount more than $500. An invoice is chosen at random and it is known that the amount

is more than $500, calculate the probability that it is paid with a credit card.

[6 marks]

(b) The Marketing Manager of a company believes that the annual sales for the next year

can be modelled by a normal distribution with a mean of $30 million and a standard

deviation of $2.5 million.

(i) What is the probability that the annual sales of next year will between $25.5

million and $36 million? [4 marks]