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CONFIDENTIAL*
2
1. A discrete random variable X has a probability distribution as shown in the table below. X= x P(X = x) (a) Find the value of n. (b) Given that E ( X ) = 1.6 , find the value of m. [1 mark] 0 0.1 m 2n 2 0.3 3 0.2
[1 mark] (c) Given that = X 1 + X 2 where X 1 and X 2 are independent random variables of X, Y find E (Y ) . [2 marks]
2. The mean height of 100 students selected randomly in a college was found to be 150 cm with a standard deviation of 5 cm. (a) E

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CONFIDENTIAL
*21. A discrete random variable
X
has a probability distribution as shown in the tablebelow.
X
=
x
0
m
2 3P(
X
=
x
) 0.1 2
n
0.3 0.2(a) Find the value of
n
.[1
mark
](b) Given that
( )
1 6
E X .
=
, find the value of
m
.[1
mark
](c) Given that
1 2
Y X X
+
where
X
1
and
X
2
( )
EY
are independent random variables of
X
,find .[2
marks
]2. The mean height of 100 students selected randomly in a college was found to be150 cm with a standard deviation of 5 cm.(a) Estimate the mean and standard deviation of the mean height of all the students inthe college.[3
marks
](b) Estimate the standard error of the mean height of the students.[2
marks
]3. The demand for tiger prawns in Malaysia depends on the price.Price per kg (RM) 27 26 25 24 23 22 21 20Sales ( ‘000kg ) 10 12 15 19 27 37 44 59Calculate the Pearson’s correlation coefficient. [5
marks
]
4. The number of laptop computers that are sold in a week by 16 representatives in atown is as follows:6 10 9 59 22 14 25 26 11 27 50 27 37 38 19 38(a) Draw a stemplot to represent the above data.[3
marks
](b) Hence, find the median and the semi-inter quartile range of this distribution.[4
marks
]
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CONFIDENTIAL
*35. The following table shows the number of digital camera sold in a departmentalstore for the year 2007 and 2008.Type of digital camera2007 2008Price(RM) Quantity Price(RM) Quantity
A
350 53 450 81
B
500 36 550 75
C
800 35 900 42
D
1200 60 1500 50By using 2007 as the base year,(a) calculate the average of relative quantity index of digital cameras
A, B, C
and
D
for the year 2008.[3
marks
](b) calculate the Paasche price index for the year 2008 and explain your answer.[3
marks
]6. Events
A
and
B
are such that
( )
13
PA
=
,
( )
3|4
P B A
=
,
( )
1'4
P A B
=
Find(a)
( )
PAB
,(b)
( )
P B
,Determine whether events
A
and
B
are independent. Give reasons for your answer.[7
marks
]7. The relationship between two variables
x
and
y
are found to be as the following:
x
15 16 17 18 19 20 21 22
y
2.4 2.5 2.6 2.6 3.0 3.5 3.6 3.4(a) Plot the scatter diagram for the above data and state the relationship between
x
and
y
.[3
marks
](b) Find the equation of the regression line of
y
on
x
in the form of
y
=
a
+
bx
,where
a
and
b
are expressed correct to two decimal places. Draw the graph of theregression line on your scatter diagram.[7
marks
]
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CONFIDENTIAL
*48. The following table shows the activities for a project and their preceding activities andduration.Activity Preceding Activities Duration (days)
A -
3
B -
3
C -
7
D A
1
E D,J
2
F B
2
G C
1
H E,F,G
1
J B
1(a) Draw an activity network for the project showing the earliest start time and thelatest start time for each activity.[6
marks
](b) State the critical path and the minimum completion time.[2
mark
]9. The table below shows the duration in minutes of 160 telephone calls made in onemonth by a trading company.(a) Calculate the mean call duration by the trading company.[2
marks
](b) Plot the cumulative frequency curve for the grouped data above.Hence, estimate the median for the durations of the telephone calls.[4
marks
](c) Describe the skewness of the distribution.[2
mark
s]Duration (minutes) Frequency0.0 – 2.9 123.0 – 5.9 336.0 – 8.9 459.0-11.9 3812.0-14.9 1915.0-17.9 718.0-20.9 6
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CONFIDENTIAL
*510. The following table shows the quarterly profits (RM’000) of a company.
YearQuarter1 2 3 4
200320042005263234445658100120122465052(a) Calculate the centred four-quarter moving averages for the above data.[4
marks
](b) Calculate the quarterly seasonal variation index using the multiplicative model.[4
marks
](c) Predict the amount of profit for the first quarter of the year 2006.[4
marks
]11. A bakery shop bakes two types of breads,
A
and
B
, which are made of three types of ingredients:
P
,
Q
and
R
. One loaf of type
A
bread needs 3 units of ingredient
P
,1 unit of ingredient
Q
and 3 units of ingredient
R.
One loaf of type
B
bread needs4 units of ingredient
P
, 2 units of ingredient
Q
and 8 units of ingredient
R.
The bakeryhas 480 units of ingredient
P
, 180 units of ingredient
Q
and 640 units of ingredient
R.
The profit for Type
A
bread is RM2.00 per loaf, whereas the profit of type
B
bread isRM3.00 per loaf.(a) Formulate the linear programming problem to obtain maximum profit.[4
marks
](b) Using the graphical method, determine the number of loaves of each type of breadthat must be baked to obtain the maximum profit and find this maximumprofit.[9
marks
]12. The mass of a type of pill produced by a pharmacy store has a normal distributionwith mean
µ
g and standard deviation 0.2 g(a) Given
7
µ
=
g, find the probability that the mean mass of a random sample of 16pills exceed 7.05g.[4
marks
](b) If the mean mass of the random sample of the 16 pills is 7.2 g, find a 96%confidence interval for the population mean,
µ
. State with reason whether themanager’s claim that
8
µ
=
g is true or false.[6
marks
](c) Determine the minimum sample size needed so that the difference between samplemean and true mean
µ
is less than 0.1 g at a 90% confidence interval.[5
marks
]
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