Question 2

(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.

(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]

(ii) Determine the annual sales that has a 10% chance of being exceeded next year. [3 marks]

(c)The customer services manager of a company receives 2 complaint calls per day on average.

(i) Calculatetheprobabilitythatthecustomerservicesmanagerreceivesatmostone complaint call in a randomly selected day. [4 marks]

(ii) Five days are randomly chosen, calculate the probability that the customer services manager receives at most one complaint call per day in two days.

[4 marks]