1 | 6 TRIAL STPM Mathematics M MethodistKL Section A [45 marks] Answer all questions in this section 1 For a project, a student asked 40 people to draw two straight lines with what they thought was an angle of 75° between them, using just a ruler and a pencil. She then measured the size of the angles that had been drawn and her data are summarised in this stem and leaf diagram 4 1 4 5 0 2 4 5 5 8 9 6 1 1 3 3 4 6 5 5 7 8 9 7 0 1 1 2 3 3 4 4 4 7 5 6 6 7 7 9 9 8 0 1 1 3 4 8 5 6 Key: 4 | 1 = 41 o (a) Find the median and quartiles of the data. [3 marks] (b) Draw a box plot representing these data on a graph paper. [3 marks] (c) Describe this distribution. [1 mark] 2 In a large restaurant, an average of 3 out of every 5 customers ask for water with their meal. A random sample of 10 customers is selected. (a) Find the probability that (i) Exactly 6 ask for water with their meal, [2 marks] (ii) Less than 9 ask for water with their meal. [3 marks] A second random sample of 50 customers is selected (b) Find the smallest value of n such that P 9 . 0 ) ( n X where the random variable X represent the number of these customers who ask for water. [3 marks] 3 For a geography project a student studied weather records kept by her school since 1993. To see if there was any evidence of global warming she worked out the mean temperature in degrees Celsius at noon for the month of June in each year. Her results are shown in the table below. Year 1993 1994 1995 1996 1997 1998 1999 2000 Mean Temperature ( o C) 21.9 24.1 20.7 23.0 24.2 22.1 22.6 23.9 (a) Plot a scatter diagram showing these data. [2 marks] The student wanted to investigate further whether or not her data provided evidence of an increase in temperature in June each year. Using Y for the number of years since 1993 and T for the mean temperature, (b) Calculate the product moment correlation coefficient for these data. [4 marks] (c) Comment on your result in relation to the student’s enquiry. [1 mark]
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1 | 6
TRIAL STPM Mathematics M MethodistKL
Section A
[45 marks]
Answer all questions in this section
1 For a project, a student asked 40 people to draw two straight lines with what they thought was an angle of
75° between them, using just a ruler and a pencil. She then measured the size of the angles that had been
drawn and her data are summarised in this stem and leaf diagram
4 1
4
5 0 2 4
5 5 8 9
6 1 1 3 3 4
6 5 5 7 8 9
7 0 1 1 2 3 3 4 4 4
7 5 6 6 7 7 9 9
8 0 1 1 3 4
8 5 6
Key: 4 | 1 = 41o
(a) Find the median and quartiles of the data. [3 marks]
(b) Draw a box plot representing these data on a graph paper. [3 marks]
(c) Describe this distribution. [1 mark]
2 In a large restaurant, an average of 3 out of every 5 customers ask for water with their meal. A random
sample of 10 customers is selected.
(a) Find the probability that
(i) Exactly 6 ask for water with their meal, [2 marks]
(ii) Less than 9 ask for water with their meal. [3 marks]
A second random sample of 50 customers is selected
(b) Find the smallest value of n such that
P 9.0)( nX
where the random variable X represent the number of these customers who ask for water.
[3 marks]
3 For a geography project a student studied weather records kept by her school since 1993. To see if there
was any evidence of global warming she worked out the mean temperature in degrees Celsius at noon for
the month of June in each year.
Her results are shown in the table below.
Year 1993 1994 1995 1996 1997 1998 1999 2000
Mean
Temperature
(oC)
21.9 24.1 20.7 23.0 24.2 22.1 22.6 23.9
(a) Plot a scatter diagram showing these data. [2 marks]
The student wanted to investigate further whether or not her data provided evidence of an
increase in temperature in June each year. Using Y for the number of years since 1993 and T for
the mean temperature,
(b) Calculate the product moment correlation coefficient for these data. [4 marks]
(c) Comment on your result in relation to the student’s enquiry. [1 mark]
2 | 6
4 A group of office workers were questioned for a health assurance policy. 5
2were found to take regular
exercise. When questioned about their eating habits 3
2said they always eat breakfast and, of those who
always eat breakfast 25
9also take regular exercise.
Find the probability that a randomly selected worker
(a) always eats breakfast and take regular exercise. [3 marks]
(b) does not always eats breakfast and does not always take regular exercise. [3 marks]
Determine, giving your reason, whether or not always eating breakfast and taking regular exercise are
statistically independent. [2 marks]
5 The wage rates paid and number of employees in each of three categories are shown below for the years
1983 and 1988.
1983 1988
Categories Wage Rate (RM) Number of
employees Wage Rate (RM
Number of
employees
A 3.80 150 4.40 200
B 3.50 250 3.90 300
C 3.00 500 3.30 400
Calculate both base and current weighted index numbers with 1983 as base to show the change in wage
rates. Explain why the results differ. [7 marks]
6 The data below showed the number of unemployed population of a certain country for the year 1988,
1989 and 1990.
Year
Number of Unemployed (Thousand)
Quarter
1 2 3 4
1988 36 24 25 30
1989 32 23 23 27
1990 28 21 20 25
If the seasonal factors based on the additive models are as follows:
Quarter
1 2 3 4
+4 -3 -3 +2
(a) Write the seasonally adjusted number for this data. [3 marks]
(b) Write the equation for the trend line and forecast the number of unemployed population for the first
quarter of the year 1991. [5 marks]
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Section B
(15 marks)
Answer any one question in this section
7 Happyholidays is a travel company which organizes package holidays that are sold through a number of
travel agents. It decides to offer the travel agents a bonus if they can increase the number of holidays sold
by 10% or more.
The number of Happyholidays holidays sold by Ajay, a travel agent is shown in the table below.