The following frequency distribution shows the selling price of 500 ml of bubble tea of all the vendors in Kepong area Selling price (RM) 4 7 Number of vendors 8 7 10 15 10 13 12 13 19 19 and above 10 5 a) State the variable of interest Indicate whether the variable is quantitative discrete, quantitative continuous or qualitative (2 marks) b) Construct a less than cumulative frequency distribution and hence draw a less than cumulative frequency polygon Use the graph to estimate (6 marks) (i) the median and interpret the result (3 marks) (ii) the minimum selling price of the top 10 high range bubble tea (2 marks) (iii) the percentage of vendors who sell below RM 16 for 500 ml of bubble tea (2 marks) c) Calculate the mean and the standard deviation of the data (7 marks) d) Calculate the coefficient of skewness and interpret the result (3 marks) Total 25 marks Question 2 a) In a college, the business school students constitute 60 of the students' population 30 of the business school students and 20 of the non business school students like the Ally bubble tea b) c) d) (i) Draw a well labelled probability tree diagram with the joint probabilities calculated to illustrate this situation (4 marks) (ii) Determine the probability that a randomly selected student likes The Ally bubble tea (iii) (3 marks) Given that a student who likes The Ally bubble tea was selected, what is the (3 marks) probability that the student is not a business school student Suppose in a class, 30 of the students like the Ally bubble tea A random sample of 12 students is selected Find the probability that 8 or 9 students do not like The Ally bubble tea (4 marks) In one day, on average, 3 customers will bring their tumblers to purchase bubble tea in The Ally Find the probability that at least 1 customer will bring his her tumbler to purchase bubble tea in The Ally on the following two days (4 marks) In The Ally, the volume of a M size bubble tea dispensed by a machine is normally distributed with a mean of 510 ml and a standard deviation of 10 ml (i) Find the probability that the volume of a M size bubble tea dispensed by the machine is more than 500 ml (4 marks) (ii) 10 of the M size bubble tea have volume less than k ml, find the value of k (3 marks) Total 25 marks Question 3 a) A vendor is interested to study the relationship between the average selling price and the sales revenue of bubble tea The survey on the popular brands of bubble tea in KL region is shown in the table below The Diger Xin Fu Bubble Tea Catime Soylap Ta boba Ti Kong Ally Sugar Dang Live Ca Average selling 9 13 9 11 5 8 5 6 5 7 5 price (RM), x Sales revenue 85 85 74 92 65 105 50 60 (RM'000), y It is given that x 78, y 616,x 803, y 49740 and xy 6286 5 b) (i) Calculate the Spearman's rank correlation coefficient (ii) (iii) (5 marks) Assuming that a linear regression model is appropriate, find the equation of the least squares regression line of y on x in the form of a bx (5 marks) Estimate the sales revenue for a new brand of bubble tea if the average selling price is RM 15 (2 marks) The following table shows the sales revenue of bubble tea (in RM thousands) achieved by The Ally over the past 3 years Sales revenue of bubble tea (in RM thousands) Year January March May July September November February April June August October December 1 14 14 5 22 12 17 2 14 17 11 22 12 20 3 14 8 11 22 12 29 (i) Compute the six point centred moving average trend (5 marks) (ii) Calculate the average seasonal variations using the additive model (4 marks) (iii) Forecast the sales revenue of bubble tea for March April in year 4 (3 marks) (iv) De seasonalise the data for January February in year 3 (1 mark) Total 25 marks Question 4 a) b) c) The quality control manager of The Ally wants to know whether the volume of the M size bubble tea dispensed by a machine is within the acceptance limits He randomly examined 100 cups of M size bubble tea dispensed by the machine and found that the mean volume is 510 ml and the standard deviation is 10 ml Find a 97 confidence interval for the population mean volume of all the M size bubble tea (5 marks) The quality control manager of The Ally claims that at most 2 of the bubble tea dispensed by a machine is less than the volume stated on the label of the cups, which is 500 ml A random sample of 100 cups is examined and found that 3 cups having less than the volume stated on the label of the cups Use 5 , test the manager's claim (9 marks) Eight years ago, Jerry invested RM 10,000 into an education fund for his daughter at the interest rate of 5 per annum compounded quarterly Find the amount of the education fund today (4 marks) d) The cost and the estimated net cash flows of a project are tabulated below Cost (RM'000) 0 100 Net cash flow (RM'000) at year end 1 40 2 3 4 40 60 50 Year Investment If the cost of capital (discount rate) is 12 per annum, calculate the net present value (NPV) for the project Decide whether it is worthwhile to invest in this project and state your reason (7 marks) Total 25 marks

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The following frequency distribution shows the selling price of 500 ml of bubble tea of all the vendors in Kepong area. Selling price (RM)

The following frequency distribution shows the selling price of 500 ml of bubble tea of all the vendors in Kepong area. Selling price (RM) 4-

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