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Section A [45 marks] Answer all questions in this section.

1.The duration of time taken by 146 players to finish a game at a particular play station is shown in the table below.Duration (minutes) Frequency

1 7 17

8 14 30

15 21 36

22 28 22

29 35 14

36 42 12

43 49 9

50 56 6

(a)Construct a histogram to display the above data. Comment on the skewness of the distribution obtained. [3 marks](b)Hence, estimate the median and mode.[4 marks](c)Calculate the percentage of the number of players who spent more than 30 minutes to finish the game.[2 marks]

2.The form six students in SMK Tinggi Klang was found that 64% of the students were females and 20.3% of the students joined the Red Crescent Society. 9.5% of the students who join Red Crescent Society were female students. A student is chosen randomly. Event A is a female student being chosen and event B is a student who joins Red Crescent Society being chosen. (a) Determine whether A and B are mutually exclusive and independent. [4 marks] (b) Find P(A'| B). [3 marks]

3.The continuous random variable X has probability density functionf (x) = Find the(a)cumulative distribution function of X.[3 marks](b)value of E(X).[3 marks](c)modal value of X.[2 marks]

4.The following table shows the revenue (quantity multiplied by price) for three types of products P, Q and R at current price and 2000 price. ProductRevenue at current price(RM million)Revenue at 2000 price (RM million)

200020132013

P60195145

Q205940

R408540

Total120339225

Calculate(a)the Laspeyres quantity index for the year 2013 by using 2000 as the base year.[3 marks](b)the percentage change in the quantity from 2000 to 2013. [1 marks](c)the Paasche price index for the year 2013 by using 2000 as the base year.[3 marks]

5.The table shows the number of occasions in a year on which 100 people had to consult the doctor. Number of times012345

Number of patients423419311

a) Show that the mean for the number of times a person has to consult the doctor is 0.9. [2 marks] b) Calculate the Poisson frequencies corresponding to this mean. [3 marks] c) Calculate the probability that someone has to consult their doctor more than thrice in a period of four years. [3 marks]

6.Tekad Sdn Bhd believes that the quarterly production trend for its product can be described by the following linear regression equation:P = 1 500 10t(100r2 = 92)where P = Total production (RM 000)and t = duration in quarter yearsThe current quarter is the third quarter 2013, and is denoted by t = 10.The average quarterly seasonal variation is as follows:Quarter yearQ1Q2Q3Q4

Seasonal variation+40% 60% 80%+100%

(a)Explain the meaning of the trend production equation of Tekad Sdn Bhd. Comment on its reliability.[3 marks](b)Predict the production in the first and second quarter in 2014.[3 marks]

Section B [15 marks]Answer any one question in this section.

7.(i) A box contains three identical balls: red, yellow and green. A game is played by selecting two balls at random, one by one with replacement, from the box. A player scores 3 points if he picks red ball, 2 points for yellow ball and 1 point for green ball. The total score from two balls is obtained. Show that a players score is a discrete random variable.[3 marks]

(ii) From past records, it is known that 3% of the total sums of an item produced in factory SUPER are defective. (a) A random sample of ten items is chosen. Find the probability that at most two items are defective. [3 marks] (b) Determine the maximum number of these items should be packed in a box such that the probability of at least one defective item is not more than 99%? [4 marks] (c) An independent random sample of 200 items are collected. Using an appropriate approximation, determine the probability that at most three items or at least eight items are defective. [5 marks]

8.A manager attempts to analyse whether the media advertisement has an impact on the customers consumption of the company product. The table below shows the weekly advertising expenditure and the customers consumption, in RM. Advertising Expenditure(RM thousands)1.523.54.55.57.59.510.51213

Consumption of the product(RM millions)234.255.566.56.877.5

(a)Draw a scatter diagram for the above data. [2 marks](b)Calculate the coefficient of determination for the regression line, and interpret your answer.[3 marks]

The manager decided to fit the model of the form y = loge (axb ), where x is the advertising expenditure, y is the consumption of the product, a and b are constants.

(c) Transform the equation to the appropriate linear form and determine the values of a and b.[4 marks](d) Calculate the coefficient of determination between the variables in (c) and comment on the result. [2 marks](e) Deduce a non-linear correlation curve between x and y.[2 marks](f) Estimate the consumption of the product for an advertising expenditure of RM 6 000? Is the result reliable? Give your reason.[2 marks]

THE END OF THE QUESTIONS

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