STPM Mathematics (M) 950/1 Trial Examination Paper
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Section A [45 marks] Answer all questions in this section.
1.
The lengths of the sixty songs recorded by a group of singers are shown in the following table: Length of a song in Number of songs seconds (x ) 1 0 x 120 120 9 120 120 x 180 15 180 x 240 17 240 x 300 13 300 x 360 5 360 x 600 (a) (b) (c)
2.
3.
Display the data in a histogram. Determine the mean length of a songs. Determine the standard deviation of the length of the songs.
The events A events A and and B B are are such that P( A| A B) |B) = 0.5, P( B| B A)=0.25, |A)=0.25, P( A B) =0.1 (a) Calculate the value of P( B). B). (b) Give a reason why A why A and and B B are not independent. (c) Calculate the value of P( A B' )
[2 marks] [1 mark ] [3 marks]
Let Pearson’s correlation coefficient between v ariables x ariables x and and y y for for a random sample be r . (a) (i) What does r measure? r measure? [1 mark ] (ii) State the range of possible values of r and and what it means when r = r = 1 [2 marks] (b) A sample of 8 data point point are summarized as follows. 470 , x 2 24479 , y 2 29450 and xy 26520 x 423 , y 470 Calculate the Pearson’s correlation coefficient and comment on your answer.
4.
A discrete random variable X has the probability distribution as follows: X 0 2 5 n 12 P( X X = x) x) p 0.25 2 p 0.3 0..15 where p where p is is a constant. (a) (b) (c)
5.
[3 marks]
Find the value of p of p.. The value of n, given that E( X ) = 5.7 Calculate the variance of X. of X.
[2 marks] [2 marks] [3 marks]
The following data shows the number of tourist (‘000) in (‘000) in the years 2011, 2012 and 2013 Year Quarter 1 Quarter 2 Quarter 3 Quarter 4 2011 22 12 110 31 2012 21 26 150 70 2013 50 36 146 110 (a) (b) (c)
Find the four-quarter centred moving average for the time series. [2 marks] Calculate the seasonal variation using an additive model. [3 marks] Use this model to predict number of tourist for the first quarter of the year 2014. [5 marks]
6.
The table below shows the unit price and the quantities of several daily food bought by a family for month of January and July. Food Rice Meat Fruit Fish Vegetable (a) (b) (c)
If the simple aggregate price index increases by 20% from January to July, determine the value of a. Calculate the Laspeyres price index, and comment on your answer. Calculate the Paasche quantity index, and comment on your answer.
Section B [15 marks] Answer any one question in this section.
7.
In an accountancy examination, 70% of the students pass the examination. (a) If 10 students were selected at random, find (i) the probability that exactly 5 students pass. (ii) the probability that at least two students pass. (iii) the expected number of students not pass. (iv) how many of them are most likely to pass. [9 marks] (b) Calculate the least number of students needed to selected at random in order that the probability of getting at least one students pass is greater than 99%. [3 marks] (c) If there are 150 students take the examination, calculate the probability that more than 50 students pass the examination. [3 marks]
8.
An advertising firm conducted a survey on television viewing habits for boys and girls. The table below shows the number of hours hours per week spent watching television by 20 boys and 18 girls. girls. Boys Girls 35 35 36 38 45 16 48 31 34 34 45 30 47 24 50 32 29 39 40 40 40 48 34 42 26 40 31 35 40 34 40 44 47 43 36 35 25 8 (a) Construct a suitable stemplot for the above data set. [3 marks] (b) Comment on the skewness of the two distributions. [2 marks] (c) Find the interquartile range of the two distributions. [3 marks] (d) Calculate the mean and the standard deviation of the number of hours spent watching television for each gentle. [6 marks] (e) Compare the dispersion of the two distributios. [1 mark ]
