STPM Trial Examination Mathematics (M) Paper 2.Full description
STPM Trial Examination Mathematics (M) Paper 2.Full description
STPM Trial Examination Mathematics (M) Paper 2.Full description
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Beberapa ahli telah melakukan penelitian untuk mengetahui korelasi antara dua sistem klasifikasi RMR dan Q system. Korelasi ini dikembangkan di lokasi yang bermacam-macam dengan karakteristi…Full description
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manual de Formel Q
biostats questions for usmle
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Descripción: Realizado en la MUNICIPALIDAD DISTRITAL DE SAN JERONIMO -CUSCO
EVALUACION
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CONFIDENTIAL* Section A [45 marks] marks]
Answer all questions in this section. 1 In an agricultural experiment, the gains in mass (in kilogram) of 100 cows during a certain period were recorded as follows: Gain in mass (kg) (kg) 5 – 9 9 10 – 10 – 14 14 15 – 15 – 19 19 20 – 20 – 24 24 25 – 25 – 29 29 30 – 30 – 34 34 35 – 35 – 39 39
Frequency 4 12 29 32 13 7 3
(a) Calculate the mean and standard deviation of the gains in mass of 100 cows. [5 marks] marks] (b) Find the percentage of the gains in mass of cows in the range of one standard deviation from the mean. [4 marks] marks] A container contains 5 green wooden blocks, 7 red wooden blocks and 8 blue wooden blocks. The blocks are identical except for their colours. John randomly selects wooden blocks from the container until a green block is selected. If John does not select a green block, he will put it back into the container and repeat the process until a green block is obtained. 2
(a) Show that the probability probability that the second second piece piece selected selected is red is
green.
21
[2 marks] marks]
80
(b) Find the probability probability that either the second second piece piece selected is red or the fourth piece piece selected selected is [6 marks] marks]
A student takes a certain route to travel to school each day. The travel times (in minutes) for the route can be assumed to be normally distributed with mean 23 and standard deviation 4. (a) Find the probability that a journey will take between 20 and 25 minutes. [3 marks] marks] (b) If the student begins his journey at 7.05 a.m. each day and the first class starts at 7.30 a.m., find the probability he will be late to school for 2 out of 5 consecutive days. [5 marks] marks] 3
A biscuit company has carried out a survey on the age of its customers and the weekly consumption of its new product of biscuits. The table below shows the weekly consumption, y of y of the company product and the age, x age, x of of the customer custome r.
4
x (year) y (gram per week)
answer.
11 13 19 26 32 42 48 60 70 66
38 46 51 58 62 62 49 34 16 8
(a)
Determine the least square regression line of
on x on x
(b) (c)
Find the non linear correlation curve between x between x and y and y.. [2 marks] marks] Determine the consumption of the biscuits for a customer of age 65. Justify your [1 mark ]
STPM Trial 950/2 *This question paper is CONFIDENTIAL until the examination is over.
[5 marks] marks]
[Turn over CONFIDENTIAL*
CONFIDENTIAL*
2
The following table shows the price and and quantity for three different brands of 1 kg packed milk powder sold at a hypermarket.
5
Price (RM) Price (RM) Brand of Milk Powder Powder 2010 2012 A 20 30 B 30 36 C 20 30 Taking 2010 as the base year, calculate (a)
(b) the Laspeyres quantity index for the year 2013 if the quantity of milk powder brand A, brand B and brand brand C sold increased increased by 5%, 10% 10% and 15% respectively respectively compared compared to the year year 2012. [4 marks] marks]
6
The time series plot below shows shows the quarterly revenues (RM’000,000) for a toy production
company from 1997 to 1999.
(a)
Comment on the trend.
[1 mark ]
(b)
State, with with a reason, whether an additive or a multiplicative model model is more suitable to
be used to decompose the time series. (c)
[2 marks] marks]
The quarterly seasonal variations for the above data are given in the table below. Quarter Seasonal variation
1
2
3
4
0.6895
k
0.6427
2.0761
(i) Determine the seasonal variation for the the second quarter, k . (ii) Interpret the seasonal variation for the fourth quarter.
[2 marks] marks] [1 mark ]
950/2 *This question paper is CONFIDENTIAL CONFIDENTIAL until the examination examination is over.
CONFIDENTIAL*
CONFIDENTIAL*
3 Section B [15 marks] marks]
Answer only one question in this section. 7
(a)
A discrete random variable X variable X has the probability distribution function , where c is a constant.
(b)
(i)
Determine the value of the constant c.
[2 marks] marks]
(ii)
Calculate the mean and variance of X. of X.
[5 marks] marks]
A continuous random variable X variable X has the cumulative cumulative distribution function as follows. x 1 0, F ( x)
(i) (ii) (iii)
ax bx 2 , 1 x 2 1, x 2
Show that
a
1
and find the value of b. 6 1 Find P( X 1 ) . 2 Find the value of m such that
P ( X
m)
[3 marks] marks] [2 marks] marks] 1 2
.
[3 marks] marks]
The table below shows the income tax collected (in million RM) quarterly and the centred moving averages from year 2011 to year 2013.
8
Year 2011
2012
2013
Quarter 1 2 3 4 1 2 3 4 1 2 3 4
Income tax (in tax (in million RM) 12 25 20 55 21 36 34 70 35 50 40 95
(a) Using a multiplicative model, calculate the adjusted seasonal index for each of the four quarters. Write down your answers correct to three decimal places. [4 marks] marks] (b) Obtain a seasonally adjusted time series. [2 marks] marks] (c) Find the equation of the trend line using the least squares method. [4 marks] marks] (d ) Hence, predict the income tax collected in the first quarter of the year 2014 such that it [5 marks] marks] exceeds the current trend by 10%.
950/2 *This question paper is CONFIDENTIAL CONFIDENTIAL until the examination examination is over.
CONFIDENTIAL*
CONFIDENTIAL*
4
950/2 *This question paper is CONFIDENTIAL CONFIDENTIAL until the examination examination is over.
CONFIDENTIAL*
CONFIDENTIAL*
5
950/2 *This question paper is CONFIDENTIAL CONFIDENTIAL until the examination examination is over.
