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Cork Institute of Technology
Higher Certificate in Science in Computing (ACCS) - Stage 1
(NFQ – Level 6)
Autumn 2007
Quantitative Analysis
(Time: 3 Hours)
Answer five questions Examiners: Ms. M. Meagher Ms. A. Brown Ms. J. English
Q1. The following table shows the turnover in millions of euros of 125 private companies in Ireland.
Turnover (millions) Number of Companies 0 and less than 50 21 50 and less than 100 25 100 and less than 150 17 150 and less than 225 30 225 and less than 300 19 300 and less than 400 9 Greater than 400 4
(a) Represent the data above on a histogram. (4 marks) (b) Calculate the mean and standard deviation for this distribution. (6 marks) (c) Calculate the mode and the median for this data. (6 marks) (d) Calculate a measure of skewness for this data. Explain your result. (4 marks)
Q2. A sample of 40 employees of a large organization yielded the following ages (in years) for the selected staff members
(a) Form a frequency distribution with 5 classes of equal width. (6 marks) (b) Represent the distribution in (a) on a Cumulative Frequency Curve. (5 marks) (c) Estimate the values of the third quartile, the median and forty fourth percentile. (6 marks) (d) How many of the employees are 49 years old or less? (3 marks)
Q3. (a) The probability that a share price rises from one day to the next is 0.65. An investor has a portfolio of ten independent shares. Calculate the probability that on a particular day: (i) at most two shares will rise. (3 marks) (ii) at least 4 shares will rise. (3 marks) (b) Through any particular working day, the average number of borrowers who queue at a college library issuing desk is three per minute. Determine the probability that in any particular minute: (i) two borrowers appear at the desk (2 marks) (ii) three or more borrowers appear at the issue desk. (3 marks) (iii) What is the probability that, in any 2.5 minute period, 4 borrowers appear at the issue desk? (2 marks) (c) Studies reveal that petrol consumption for small cars follows a normal distribution with a mean of 12.0 km. per litre and the standard deviation is 2.4. What percentage of small cars is expected to have a petrol consumption of: (i) less than 8.7 km. per litre? (2 marks) (ii) more than 14.6 km. per litre? (2 marks) (iii) between 8.7 and 14.8 km. per litre? (3 marks)
Q5. The following table shows the quarterly sales (0000’s) of a company for the years 2003-2006.
Sales(€000’s) YEAR Q1 Q2 Q 2003 24 25 27 2004 20 23 26 2005 17 18 22 2006 21 22 24
(a) Plot the data above on a time series graph. (4 marks) (b) Calculate a moving average for the data and plot the trend line on the graph of part (i). (6 marks) (c) Using the additive model, calculate a seasonal index for each of the four periods. (7 marks) (d) Forecast the sales for the first two quarters of 2007 for the above company. (3 marks)
Q6. (a) A company has the following demand and cost functions for a particular item. Demand Function: pr = 450 – 3x Cost Function: C = 120 +200x Where pr is the price of the item, x is the quantity produced (in 00’s) and sold and C is the total cost (in 00’s) of producing the item. (i) Determine the quantity to maximize profit and calculate the maximum profit. (4 marks) (ii) Calculate the value(s) of x which would be known as the ‘break-even’ points. (4 marks) (b) In a machine shop a company manufactures two types of electronic component, on which it aims to maximize the contribution to profit. The company wishes to know the ideal combination of X and Y to manufacture. All the electronic components are produced in 3 main stages: Assembly, Inspection & Testing and Packing. The number of minutes required for each unit is shown as follows:
In total, there are 280 hours available for assembly and 100 hours available for inspection and testing each week. At all stages both components can be processed at the same time. At the final stage the components require careful packaging prior to delivery. There is a total of 60 packaging hours available each week. The contribution on X is 12 per unit and on Y is 20 per unit. For engineering reasons, not more than 450 of X can be made in any one week. All production can be sold. You are required to: (i) state all of the inequalities (constraints) which describe the production conditions. (3 marks) (ii) graph these constraints. (5 marks) (iii) find how many of products X and Y should be produced to maximize contribution. (4 marks)
Assembly (mins) Inspection&Testing (mins)
Packing (mins) X 30 10 15 Y 40 30 20
