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TRIAL EXAMINATION

2013

MATHEMATICS MPaper 21 hours

Instruc t ions to al l candidates:

Answer all questions in Section A and any one question in Section B. Answers may be written in

either English or Bahasa Malaysia.

All necessary working should be shown clearly.

Scientific calculators may be used. Programmable and graphic display calculators are prohibited.A list of mathematical formulae, statistical tables and graph papers are provided on pages of this

question paper.Section A [45 marks]

Answer all questions in this section.1. In a garden, 25% of the pots are sunflowers. For a sample of 6 pots selected at random

from the garden, find the probability that

(i) exactly 3 pots are sunflowers. [2]

(ii) at least 4 pots are sunflowers. [3]

2. An opinion poll on a certain political party is conducted on 1000 voters, of whom 600 are

males. It is found that 250 voters are in favour of the party. It is also found that 450 male

voters are not in favour of the party.

(a) Find the probability that a randomly chosen voter is in favour of the party if the voter is

a female. [1]

(b) Find the probability that a randomly selected voter is a male or not in favour of the

party. [2]

(c) Determine whether the events a voter is a male and a voter is in favour of the party

are independent. [3

3. Xand Y are events such that P(X) = , P(X/Y) =2

3, and P(X/Y)=

3

7. Find P(XY), P(XY),

P(Y) and P(Y/X)

Based on the information obtained, state with reason whether events Xand Y are

(a) independent (b) mutually exclusive.

[6]

[3]

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4. A continuous random variable X has cumulative distribution functionF(x)given by

8,

84,

10

140,

0,0

)(

xd

xcx

xbax

x

xF

(a) Determine the values of the constants a, b, cand d. [4 marks]

(b) Sketch the graph of F(x) [3 marks]

(c) Find the probability density function,f(x). [4 marks]

(d) Find P( 3

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i) Calculate the median weight of the students. [3 marks]

ii) Plot a cumulative frequency curve of the above data. [3 marks]

iii) Using your graph, estimate the percentage of students whose weight lies within

one standard deviation from the mean. [5 marks]

Section B [15 marks]

Answer any one question in this section.

7. Amy Company believes that the quarterly sales trend for its production can be

expressed in the linear regression equation as follow:-

T = 409 + 11 t

t 1 2 3 4 5 6 7 8 9 10 11

S 400 430 490 440 420 535 490 460 480 550 530

S represents the sales and t= 1 to 11 represents times from the first quarter of 2005 to the

third quarter of 2007.

(i) Plot the time series and comment on the trend. [3 marks]

(ii) Use the given regression equation, find the trend values from t=1 to t=11. [3 marks]

(iii) Find the seasonal variations using an additive model. [6 marks]

(iv) Estimate the sales for fourth quarter of the year 2007 and first quarter of year

2008. [3 marks]

8.

[4 marks]