(a) A company claims it puts an average of 1litre in its milk bottles labelled as such. A random sample of 10 bottles was picked and revealed content (in millilitres).

990

998

1000

1001

999

995

1002

999

1000

996

Assume a normally distributed population. Based on this sample, do you believe the company's claim at =0.01?

Use an appropriate one-sided test. Clearly state the null and alternative hypotheses, test statistic and conclusions.

(b) The daily returns of stock A in 6 consecutive trading days are shown in the table below.

Day	1	2	3	4	5	6
return	1.5%	-0.5%	-1.0%	1.2%	1.1%	2.0%

(i) Use single exponential smoothing to forecast the stock return on Day 7.Use a damping factor of 0.06.

(ii) Use a 3-day moving average method to forecast the stock return on Day 7.

(c) Flaws appear in sheets of glass randomly at an average of one flaw every 3 square metres. Find the probability that a sheet of glass with the dimension 5m*5m has no flaws.