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Introduction To Business Statistics Question Paper
Introduction To Business Statistics
Course:Bachelor Of Commerce
Institution: Strathmore University question papers
Exam Year:2011
1
STRATHMORE UNIVERSITY
SCHOOL OF MANAGEMENT AND COMMERCE
Bachelor of Commerce
MAT 2102: INTRODUCTION TO BUSINESS STATISTICS
END OF SEMESTER EXAMINATION
DATE: 23RD MARCH 2011 TIME:2HRS
INSTRUCTION: Answer Question One and any Other Two Questions
Question 1 (30 Marks)
(a) Differentiate between the following terms as applied in statistics
(i) Discrete and continuous random variable [2 Marks]
(ii) Inferential statistics and descriptive statistics [2 marks]
(iii) An event and an experiment [2 Marks]
(b) X and Y are two independent events such that P(X/Y) =0.4, P(Y) =0.25 and
P(X) =0.2
Find; (i) P(X nY) (ii) P(X ?Y) [4 Marks]
(c) The amount of time consumed by an individual at a bank ATM is found to be
normally distributed with mean µ =130 seconds and standard deviation
s = 45 seconds. Find
(i) the probability that a randomly selected individual will consume less than
100 seconds at the ATM [3 Marks]
(ii) the probability that a randomly selected individual will spend between 2
to 3 minutes at the ATM [4 Marks]
(d) The marks obtained by sixty candidates in an examination were as follows:
Plot a histogram and a frequency polygon on the same graph to represent the data
[6 Marks]
Marks 20-29 30-39 40-49 50-59 60-69 70-79
Number of candidates 4 10 16 19 8 3
2
(e) In the year 2002, a cooperative society began down sizing in order to reduce its
costs. One of the results of these cost cutting measures has been a decline in the
percentage of managerial jobs. The following data shows the percentage of
females who were managers from 2002 to 2009.
Calculate
(i) 3-year moving average [3 Marks]
(ii) The semi-moving average and use it to estimate the percentage female
managers in the year 2010. [4 marks]
Question 2 (20 Marks)
The daily expenditure in $ of 100 families is given below
Daily
expenditure, $
0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80
Number of
families
2 7 21 25 30 35 28 12
Using an assumed mean of $35.5, Determine:
a) The Monthly average amount spent by each family [5 Marks]
b)Variance [4 Marks]
c) Standard deviation [2 Marks]
d)Mode [5 Marks]
e) The second Quartile [4 Marks]
Question 3 (20 Marks)
(a) A University student studying the employment situation in a certain town found
out that the probabilities of males and females who are employed is as shown in
the table below.
Years 2002 2003 2004 2005 2006 2007 2008 2009
Percentage 5.9 5.1 4.2 6.3 6.0 7.4 5.3 6.0
3
Employed Unemployed
Males 0.40 0.10
Females 0.475 0.025
Suppose an unemployed person is chosen at random. Find the probability that the
person selected is
(i) Male [3 Marks]
(ii) Female [3 Marks]
(b) The probability that a contractor will get a plumbing a contract is 2 3 and the
probability that he will not get electrical contract is 9
5 . If the probability of
getting at least one contract is 5
4 Find the probability that he will get both?
[4 Marks]
(c) Differentiate between positive and negative correlation [2 Marks]
(d) A company is introducing a job evaluation scheme in which all jobs are graded by
points for skill, responsibility and so on. Monthly pay scales (in thousand Kenya
shillings) are then drawn up according to the number of points allocated. To date,
the company has applied this scheme to 9 jobs:
Job A B C D E F G H I
Points 5 25 7 19 10 12 15 28 16
Pay 3.0 5.0 3.25 6.5 5.5 5.6 6.0 7.2 6.1
(i) Determine correlation coefficient between points allocated and monthly pay using
the rank correlation method. [ 6 Marks]
(ii) Comment on the nature of correlation [2 Marks]
Question 4 (20 Marks)
(a) Explain any TWO limitations of time series analysis [4 Marks]
(b) Briefly explain two application areas of time series in business [4 Marks]
(c) The table below gives the monthly income and expenditure on food of seven
households.
4
Income (x) 35 49 21 39 15 28 25
Food expenditure
(y)
9 15 7 11 5 8 9
(i) Fit the least square regression line for the data on incomes and food expenditures.
Take income as independent variable and food expenditure as a dependent
variable. [9 Marks]
(i) Find how much a household with a monthly income of $3500 spends on food
[3 Marks]
Question 5 (20 Marks).
(a)The demand for a product of a local company varies greatly from month to month. The
probability distribution is given in the table below
Unit demanded Probability
300 0.20
400 0.30
500 0.35
600 0.15
Determine
(i) Expected monthly demands [2 Marks]
(ii) The variance of the monthly demands [4 Marks]
(iii)If Y = 2x +1, determine the variance of Y [3 Marks]
(b) Give two conditions for a function f (x) of a continuous random variable X to
be a probability density. [2 Marks]
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