NATIONAL OPEN UNIVERSITY OF NIGERIA

UNIVERSITY VILLAGE, PLOT 91, CASDASTRAL ZONE, NNAMDI AZIKIWE EXPRESS WAY, JABI, ABUJA.
FACULTY OF MANAGEMENT SCIENCES
JANUARY/FEBRUARY 2013 EXAMINATION

COURSE CODE:       MBA 816                                                         CREDIT UNITS: 2

COURSE TITLE:       BASIC MATHEMATICS AND STATISTICS FOR MANAGERS

TIME ALLOWED:    2 HOURS

Instructions: 1. Attempt question number one (1) and any other two (2).

                       2. Question number 1 is compulsory and carries 30 marks  while  the other 2 questions carry 20 marks each.

                     3. Present all your points in coherent and orderly manner.

.

1(a)  A Ship travels between two ports.  The cost of fuel is 100(ax + b/x + 10) naira, where x is the average speed of the Ship in knots, and a and b are constants.  If the Ship travels at 4 knots, the cost of fuel would be N9,000, but at 6 knots, the cost would be N7,000.

(i) Find the values of a and b

(ii) What is the cost of fuel at an average speed of 5 knots? (15 marks)

(b) The followings are data on the number of stores that purchase bottled water in the cities as listed:  Sokoto 25,000        Lagos  20,000      Enugu  20,000      Port Harcourt   5,000, summarise these information using a pie chart. (15 marks)

2.  The followings are data on annual gross revenue of a Company:

Year        t            Gross Revenue           ty                               t²

                               (N’millIons)

                                   (y)

1987        1                    13.0                  13                              1

1988        2                    14.1                  28.2                           4

1989        3                    15.7                  47.1                            9

1990        4                    17.0                  68                             16

1991        5                    18.4                  92                             25

1992        6                    20.9                 125.4                         36

1993        7                    23.5                 164.5                         49

1994        8                    26.2                 209.6                         64

1995        9                    29.0                 261                            81

1996       10                   32.8                 328                          100

     åt  =  55              åy = 210.6     åty = 1336.8      åt²  =  385

(a) Sketch the data on your answer script

(b) Compute the regression equation, using y as dependent variable and t as independent variable.

(c) Find the trend forecasts for the years 1999, 2001, 2004, and 2006  (20 marks)

3(a) The annual income of a bank clerk is N240,000.  His income tax is charged at 10 percent, and the employer deducts 5 percent for the Pension fund.  Calculate the clerk’s net monthly income.

(b) Using the expression for the nth term of a geometric progression, compute the 8^th term of the geometric progression: 72, -24, 8, … (20 marks)

4. Given the income distribution of a sample of 50 MTN customers as follows:

Income            Number of

(N’000s)          Subscriber

20 – 30                      20

31 – 41                     15

42 – 52                     10

53 – 63                       5

(a) Compute the arithmetic mean of the incomes;

(b) Compute the Median income (20 marks)

5.  A total of N10,000 was invested in two business ventures, A and B.  At the end of the first year, A and B yielded returns on the original investments of 6 percent and 5.75 percent respectively.  How was the original amount allocated if the total amount earned was N588.75? (20 marks)