[45 marks] marks] Section A [45 Answer all questions in this section. 1
The table below records the weight loss, in kilograms, of each of 150 people people attending a dietary clinic. Weight loss (kg) 2
x
1
1
x
0
0
x
1
1
x
2
x
2 x 3 3 x 5 5 x 10
2
3
Number of people 3 7 12 19 38 46 25
(a) What do you think the negative values indicate?
[1]
(b) Obtain estimates of the values of (i) the mean, (ii) the standard deviation
[5]
(c) Present the data in a cumulative frequency graph, hence, estimate the median.
[4]
(d) Find the Pearson’s coefficient of skewness, and comment on your result.
[3]
A shop keeper found found that 30% of the customers patronized the shop would buy a book. book. The probability that a customer will buy a pen after he has bought a book is 0.6. However the probability that a customer will just just buy a pen is 0.2. Find the probability probabil ity that a customer patronizes the shop will buy (a) a book and a pen, (b) a book or a pen, (c) a pen but not a book.
[6]
Kathy finds that when she takes a cutting cutting from a particular plant, the probability probabilit y that it it roots successfully is
1
.
3
She takes nine cuttings. Find the probability probabilit y that (a) more than five cuttings root successfully, (b) at least one cuttings root successfully.
[5]
4
(a) Eight pairs of values obtained from random observations observations on two variables x and y are (4, 63), (2, 89), (5, 58), (3, 73), (4, 72), (5, 48), (3, 75) and (2, 84). (i) Plot these values values on a scatter diagram. (ii) State, with a reason, whether whether the scatter diagram in (i) displays a positive or or a negative correlation. (b) The mathematics mathematics score ( x) x) and economics score ( y ( y)) for eight students are summarized as follows.
x 448, y 472, xy 26762, ( x x)
2
[4]
2222, and and ( y y) 2110 2
Find the correlation coefficient for the scores of the two subjects, and comment on your result. [5] 5
A company produces three models of computers, model A model A,, B and B and C . The average selling price and and the number number of computers computers produced produced and sold for the years 2008 and 2013 are shown in the following table.
Year 2008 2013
6
Model A Model A Quantity Price (‘000) (RM’000) 3 10 12
4
Model B Model B Quantity Price (‘000) (RM’000) 12 15 20
8
Model C Quantity Price (‘000) (RM’000) 6 16 12
9
(a) Taking 2008 as the base year, calculate the Laspeyres and Paasche price indices for the year 2013. (b) Give a reason why the the Laspeyres and Paasche price indices are different. . The following data shows the tax (RM’000s) received by the local government.
Year
2011
2012
2013
Quarter 1 2 3 4 1 2 3 4 1 2 3 4
Tax received (RM thousand) 2.8 4.2 3.0 4.6 3.0 4.2 3.5 5.0 3.0 4.7 3.6 5.3
[4] [1]
Centred moving average
3.68 3.70 3.76 3.88 3.93 3.99 4.06 4.11
(a) Calculate the seasonal index for each quarter using an additive model. (b) Obtain a seasonally adjusted time series.
[5] [2]
[15 marks] marks] Section B [15 Answer any one question in this section. 7
A manufacturer stores drums of chemicals. During storage, evaporation takes place. A random sample of 10 drums was taken and the time in storage, x weeks, x weeks, and the evaporation loss, y loss, y ml, ml, are shown in the table below. x y
3 36
5 50
6 53
8 61
10 69
12 79
13 82
15 90
16 88
18 96
(a) Draw a scatter diagram to represent these data. (b) Give a reason to support fitting a regression model of the form y = y = a + bx to bx to these data. (c) Find, to 2 decimal places, the value of a and the value of b. (You may use .) (d) Give an interpretation of the value b. (e) Using your model, predict the amount of evaporation that would take place after (i) 19 weeks, (ii) 35 weeks. Comment on the reliability of each of your predictions.
∑ =1352, ∑ = 5311 531122 ∑ =8354
[3] [1] [4] [1]
[2] [4]
8
(a)
The diagrams show the graphs of two functions, g and h. For each of the functions g and h, give a reason why it cannot be a probability density function.
[2]
(b) The distance, in kilometres, travelled in a given time by a cyclist is represented by the continuous random variable X variable X with probability density function given by
30 10≤≤15 () = { 0 ℎ
(i) Find the cumulative distribution function, F(x). function, F(x). Sketch the graphs of f(x) of f(x) and and F(x). (ii) Show that E( X ) = 30 ln 1.5. (iii) Find the median of X of X . Find also the probability that X lies between the median and the mean.
[5] [3] [5]
