NCUK International Year One Business IDBQM001 Quantitative Methods for Business PDF 2023-2024 Exam Paper

IDBQM001 Quantitative Methods for Business NCUK INTERNATIONAL YEAR ONE BUSINESS IDBQM001 Quantitative Methods for Business 2023-2024 Examination Session...

IDBQM001 Quantitative Methods for Business NCUK INTERNATIONAL YEAR ONE BUSINESS IDBQM001 Quantitative Methods for Business 2023-2024 Examination Session Time Allowed Semester 2 2 hour 40 minutes (including 10 minutes reading time) INSTRUCTIONS TO STUDENTS SECTION A Answer ALL questions. This section carries 35 marks. SECTION B Answer 2 questions ONLY. This section carries 40 marks. The marks for each question are indicated in square brackets [ ]. The total mark for this paper is 75. Answers must not be written during the first 10 minutes. An approved calculator may be used in the examination. Show ALL workings in your answer booklet. Examination materials must not be removed from the examination room. DO NOT OPEN THIS QUESTION PAPER UNTIL INSTRUCTED BY THE INVIGILATOR V1 2324 © 2023 Northern Consortium Ltd. Page 1 of 7  IDBQM001 Quantitative Methods for Business Section A Answer ALL Questions Question A1 A shop has a stock of 50 products it wants to get rid of. The 50 products have an average price £200.00. (a) The shop decides to have a sale and marks the products down by 15%. What will be the new average price of all the products? (b) The shop decides to add more items to the sale. Their pre-sale price are below: £135 £162 £148 £187. Calculate the average price of the products once the new items have been added and their price reduced. Question A2 Give the definition of the market equilibrium for supply and demand. The supply and demand functions for a good are given by 𝑄𝑠 = 3𝑃 − 120 𝑄𝐷 = 600 − 2𝑃 where 𝑄 is the quantity in thousands and 𝑃 is the price in pounds. Find the market equilibrium. Question A3 The Pearson correlation coefficient for variables 𝑋 and 𝑌 is 0.60. Sketch a scatter diagram and a possible regression line of 𝑌 on 𝑋 illustrating this coefficient. Question A4 The profit function for 𝑥 is given by 𝑃(𝑞) = 80𝑞 + 150𝑞 2 − 14𝑞 3 where 𝑞 is the quantity of 𝑥 sold. (a) Determine the value of 𝑞 resulting in the largest profit. V1 2324 © 2023 Northern Consortium Ltd. Page 2 of 7  IDBQM001 Quantitative Methods for Business (b) Determine at what value of 𝑞 it is no longer profitable to produce 𝑥. Question A5 A basket consisting of three goods is such that in the year 2021 they have an average cost of £159, £76 and £59; the following year, their costs are £162, £69 and £64. The relative amounts sold the second year are 5, 24 and 10 respectively. Calculate and interpret the Paasche index for this basket of goods. Question A6 The marginal cost function for production quantity 𝑄 of a good is 𝑀𝐶(𝑄) = 800 − 4𝑄. Given that the maximum total cost is £100000, find the fixed cost. V1 2324 © 2023 Northern Consortium Ltd. Page 3 of 7  IDBQM001 Quantitative Methods for Business Section B Answer TWO questions ONLY Question B1 The marks on a standardized test taken by 5000 students are shown below. Mark Frequency 0 ≤ ℎ ≤ 30 250 30 < ℎ ≤ 40 100 40 < ℎ ≤ 50 1800 50< ℎ ≤ 60 2100 60< ℎ ≤ 70 375 70 < ℎ ≤ 100 375 (a) Estimate the mean, ℎ̅. (b) Estimate the standard deviation, 𝜎. Comment on your result. (c) Skewness can be measured by Pearson’s Skewness Coefficient, which is given by: ̅ −𝑚𝑒𝑑𝑖𝑎𝑛) 3(ℎ 𝑝=. 𝜎 Calculate the skewness for the data using Pearson’s Skewness Coefficient. (d) The examiners aim to have at least 80% of students achieve a mark between 35 and 75. Has this been achieved? Question B2 (a) The covariances and means for data sets 𝑋 and 𝑌 are given below. 𝐶𝑜𝑣(𝑋, 𝑋) = 20825 𝐶𝑜𝑣(𝑌, 𝑌) = 258538.2724 𝐶𝑜𝑣(𝑋, 𝑌) = 50950.5 𝑋̅ = 255 𝑌̅ = 710.26 (i) Calculate and interpret the equation of the regression line of 𝑦 on 𝑥. (ii) Calculate and interpret the correlation coefficient between variables 𝑦 and 𝑥. Comment on the reliability of your answer to (i) in terms making predictions V1 2324 © 2023 Northern Consortium Ltd. Page 4 of 7  IDBQM001 Quantitative Methods for Business on 𝑌 base on 𝑋. (b) Compare the three scatter diagrams and regression lines: A B V1 2324 © 2023 Northern Consortium Ltd. Page 5 of 7  IDBQM001 Quantitative Methods for Business C Answer the questions below, giving your reason. (i) Which diagram shows a negative correlation? (ii) Which diagram shows the weakest correlation? (iii) Which diagram shows the strongest correlation? (iv) Match the sets of variables to the equation that fits their regression line most closely. In each case justify your answer: (1) 𝑈 = −1.5𝑉 + 300 (2) 𝑈 = 0.2𝑉 + 2000 (3) 𝑈 = 2.5𝑉 + 85 Question B3 (a) The elasticity of demand for a demand function is given by: 𝑑𝐷(𝑝) −𝑝 𝑑𝑝 𝐸(𝑝) = 𝐷(𝑝) (i) Find the demand function 𝐷(𝑝) for good 𝑥 given that V1 2324 © 2023 Northern Consortium Ltd. Page 6 of 7  IDBQM001 Quantitative Methods for Business 1 30 𝐸(𝑝) = − 𝑝 , 𝐷 (𝑒 2) = 90. ln30 (ii) Find the revenue function in terms of the quantity demanded 𝑞 in thousand units. (b) Find maximum revenue and the value of 𝑞 where it occurs. - This is the end of the examination - V1 2324 © 2023 Northern Consortium Ltd. Page 7 of 7