Stpm Trial 2009 Maths2 Q&A (n9)

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papercollection 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 ] papercollection   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 ] papercollection   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 papercollection   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 ] papercollection 
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