Question 1

(a) Explain the term 'tables' in terms of summarising raw data. (2 marks)

(b)A dairy sold milk, in liters, on a daily basis for a period of 24 days

Required:

1. (i)Using a uniform class interval and starting with the class 20-24; construct a frequency distribution for the data above.
2. (2 marks)
3. (ii)Calculate the standard deviation for the data. (7 marks)

A beverages company produced and sold crates of dry gin in the years

2016 and 2017 as shown in the following table.

Month 2016 2017 January 20 30 February 50 40 March 30 50 April 40 40 May 60 50 June 100 90 July 70 110 August 90 120 September 60 80 October 80 100 November 50 70 December 120 110

Required:

(c) (i)Construct a Z-chart for the above data.

(ii)Comment on any feature in the Z-chart you have drawn.

Question 2

Mongoli Enterprises Ltd (NEL) deals in solar products. A routine visit by Uganda National Bureau of Standards (UNBS) established that the lifetime of the solar panels NEL sold was normally distributed with a mean of 25 years and standard deviation of 4 years. A quality controller from UNBS later visited NEL, tested a sample of solar panels and picked one at random.

Required: Determine the:

(i)probability that its lifetime is greater than 18 years. (3 marks)

(ii) probability that its lifetime is between 18 and 28 years. (3 marks)

(iii) sample size of the panels that were tested if only two failed to exceed a life time of 18 years.

(3 marks)

1. (b)Zakaria, a teller at Eurit Bank handles clients with bulk transactions. On a certain day, he examined a random sample of 9 transactions and noted that the mean and variance of the sample were Shs 15.2 million and Shs 5 million respectively.
2. Required:
3. Determine the range of the average transaction at 95% confidence level.
4. (4 marks)
5. (c)Tuge Ltd sells on average 3 motorcycles daily and the sales are believed to follow a Poisson distribution.

Required:

Find the probability that the motorcycle sales are:

1. (i)exactly two.
2. (ii)at most one.
3. (iii)at least two.

(2 marks) (3 marks) (2 marks)

Question 3

(a) Explain any one application of a regression line. (1 mark)

(b)The maize yield on a farm is believed to depend on the amount of rainfall. The values of the yield Q (tons per acre) and the rainfall P (in mm) for seven successive seasons are given in the table below.

Required:

(i) Compute the product-moment correlation coefficient between rainfall

and yield. (9 marks)

(ii) Comment on the result obtained in (b) (i) above. (1 mark)

A sample of six households were interviewed regarding their incomes (x)

and expenditure (y). The results (in Shs '000') are as shown below: x 230 340 370 380 140 280

y 80 90 160 180 050 070 Required:

1. (i)Determine the regression equation relating y to x. (8 marks)
2. (ii)Find the income of a household with an expenditure of Shs 60,000.
3. (1 mark) (Total 20 marks)

Question 4

1. (a)A roofing materials company produces ridges ( x ) and iron sheets ( y ) using resources according to the production function given
2. by:xy2 4y20. Required:
3. Determine the number of ridges and iron sheets produced given that for every 4 iron sheets, 1 ridge is produced.
4. (5 marks)
5. (b)A famous writer of project planning textbooks would like to be paid a royalty of 15% of the sales revenue and insists the price should maximise total revenue. On the other hand the publishing company is interested in maximising profit. Given the total revenue and total cost functions are
6. R(q)10,000q10q2 and C(q)1,0002,500q5q2 respectively, where q is the number of textbooks sold.

Required:

Determine the:

1. (i)output that maximises total revenue and obtain the maximum royalty.
2. (5 marks)
3. (ii)output that maximises profit and associated royalty at that output.
4. (6 marks)

(c) The approximate sales, in thousands of shillings, for a small retail shop in a given week are given in the probability distribution table below:

Sales (x) 100 105 110 115 120 Probability ( p ) 0.01 0.08 0.20 0.50 0.21

Required:

Calculate the variance for the distribution.

(4 marks)

Question 5

1. (a)Explain any two limitations of linear programming. (2 marks)
2. (b)Airplanes from YK airport sometimes delay to take off. The quality control manager decided to randomly choose 5 flights per day for eight days. The table below shows the number of minutes that the planes were late for
3. takeoff.
4. Day1 Day2 Day3 Day4 Day5 Day6 Day7 Day8 17 05 12 04 03 10 02 03 03 14 05 21 09 22 14 05 22 04 06 08 15 40 13 23 06 13 08 05 35 26 08 33 24 14 04 19 05 23 12 23
5. Required:
6. (i)Draw a control chart for the range for the above information.
7. (8 marks)
8. (ii)Given that the coefficients for the upper control and the lower control limits are 2.114 and 0 respectively; determine whether the process is out of control.
9. (1 mark)
10. (c)An employer wants to recruit experienced workers (x) and those on probation (y) for his firm. The firm can accommodate at most 9 workers. On average, 5 hours and 3 hours of work are required of the experienced workers and those on probation respectively. The employer has to maintain an output of at least 30 hours of work per day. The rules and regulations demand that the number of experienced workers recruited should not be more than 5 times the number of those on probation. The workers union, however, emphasizes that the number of experienced workers recruited should be at least twice the number of those on probation.
11. Required:
12. (i)Formulate linear inequalities from the information given. (4 marks)
13. (ii)Illustrate the above information on a graph. (4 marks)
14. (iii) Obtain all the possible combinations of workers that may be
15. recruited.
16. (1 mark) (Total 20 marks)

Question 6

(a) (b)

Distinguish between normal costs and crash costs under network analysis.

(2 marks)

KA Construction Ltd is in the process of designing an improved drainage system in one of the suburbs of Kampala. The activities and duration times required are listed in precedence table below:

Activity Preceding activity Duration (days) A-6 BA8 CA7

D C 12 EB3 FD5 G E,F 7

Required:

(i)Draw an activity network.

(ii)List the possible paths through the network and their duration. (4 marks)

(iii)Identify the critical path and justify your answer. (2 marks)

(iv)Distinguish between the fixed base and chain base methods of computing index numbers. (2 marks)

(v)Explain three limitations of consumer price index numbers.

(3 marks)

The table below shows the average prices (in Shs '000') for a ton of each of the following commodities in 2016 and 2017.

Commodities Maize

Beans Sorghum Millet

Required:

Prices in 2016 600

850

520

550

Prices in 2017 700

900

500

620

(i)Calculate the simple aggregate price index for 2017 using 2016 as the base year and comment on your results.

(5 marks)