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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:2007
1
STRATHMORE UNIVERSITY
FACULTY OF COMMERCE
Bachelor of Commerce
END OF SEMESTER EXAMINATION
(READING ROOM)
MAT 2102: INTRODUCTION TO BUSINESS STATISTICS
Date: 19th October 2007 Time: 2 Hours
INSTRUCTIONS: ANSWER QUESTION ONE AND ANY OTHER TWO
QUESTIONS.
QUESTION ONE (30 marks)
a) Define the following terms (i) Standard deviation(ii) mode (iii) median
(6 marks)
b) In a survey of a sample of interest rates on mortgages for 15-year mortgages at local
lending banks was found to be: 7.1%, 7.0%, 8.0%, 9.9%, 6.5%, 7.0%, 6.5%, 7.3%, 8.8%
Calculate and interpret (i) the mean (ii) median (iii) mode (iv) variance (v) standard
deviation (6 marks)
(c) (i) Different sizes of men’s trousers were sold at KSh. 1650, 1750 or 1850. There
are 50 trousers; 20 were sold at 1650 rate, 16 were sold at 1750 and 14 were sold at
1850 rate.
Find the mean selling price of the trousers. (2 marks)
(ii) A sample of weights of fifteen employees is given as: 60, 62, 79, 70, 21, 74, 62,
90, 58, 70, 65, 64, 71, 64, 60. Compute the (i) mean weights (ii) mean absolute deviation
(iii) verify that å(x - x) = 0 (4 marks)
(d) Let A and B be events with P (A) = 3/8, P (B) = ½ and P (AnB) = ¼.
Find (i) P (AUB) (ii) P (A) (iii) P (Bc) (iv) P (AcnBc) (6 marks)
(e) The following is a stem-and-leaf distribution.
Stem Leave
2
3
5
7
32 35 39 40 70
24 47 55 62 71
9 21 31 40 57 62 83
12 16 35 44 92
2
Required (i) how many values were in the original data set
(ii) Form the original values of the data set (4 marks)
(f) If the mean = 20 and standard deviation = 10, find (i) P (20 < X< 30)
(ii) P(X< 8) (2 marks)
QUESTION TWO (20 marks)
(a) The following measures of central tendency were derived from three data sets.
mean = 40, median = 36, mode = 34,
mean = 36, median = 36, mode = 36
mean = 30 median = 36 mode = 38
Required: (i) Illustrate the shapes of the distributions by drawing these facts on the same
scale
(ii) Describe the distributions in terms of symmetry, indicating the directions
of skewness of symmetric distribution: (8 marks)
(b) The following is a frequency distribution of the wages of employees at manufacturing
company:
Weekly wages (K£’000) Number of Employees
31 – 36 6
36 – 41 8
41 – 46 12
46 – 51 18
51 – 56 25
56 – 61 30
61 – 66 24
66 – 71 14
71- 75 6
75 – 81 3
(i) Construct a histogram and a frequency polygon
(ii) Construct a cumulative frequency distribution and the ogive on different
scales
(iii) Estimate and interpret the median and the mode of the distribution
(12 marks)
QUESTION THREE (20 marks)
(a) State the properties of a random variable X with probability density function f(x)
(6 marks)
(b) A small bed and breakfast establishment has two twin rooms. Daily profits depend
on the company, where £5 is made with one guest, £10 with 2 guests, £22 with three
guests or £45 with four guests. The probabilities of guests requiring rooms are: P (1
guest) = 0.15, P (2 guests) = 0.45, P (3 guests) = 0.3 and P (4 guests) = 0.1.
3
Required:
(i) Find the expected daily profit
(ii) Find the probability that at least two guests will require rooms
(iii) Find the profit for at least two quests will require the rooms.
(iv) Find the variance of the profits (8 marks)
(c) A company has to choose between two alternative products. Product A is estimated to
have a 0.45 likelihood of success while product B has a 0.6 probability of success. If
product A is successful, it will make a profit of £9,000 for the company. If it’s a failure, it
will make a loss of £2100. Product B will give a profit of £7500 if it is successful and a
loss of £1500 if it is not.
Required: (i) Compute the expected value for each product.
(ii) which product should the company launch? (6 marks)
QUESTION FOUR (20 marks)
(a) A sample of amount paid for waiting charges fixed by a taxi owner on a Saturday
in town was organized into the frequency distribution:
Amount paid Number of cars
20 – 40 4
40 – 60 9
60 – 80 15
80 – 100 28
100– 120 14
120– 140 9
140 – 160 1
160 – 180 1
Calculate (i) Range
(ii) mean amount charged
(iii) mean absolute deviation
(iv) variance and
(v) (v) standard deviation. (12 marks)
(b) James Kofu is a director of personnel services for a large organization in Nairobi.
He must hire a secretary based on typing efficiency. One candidate for the post typed
a manuscript six times with the following mistakes 5, 6, 2, 1, 2, and 0. Another
candidate typed with the following mistakes: 3, 4, 5, 3, 4, and 5.
Find (i) the mean for each candidate
(ii) the variance and standard deviation for each candidate
(iii)Which typist should the be hired (8 marks)
4
QUESTION FIVE (20 marks)
(a) The price of a motor spare part at given outlet stores throughout a town are shown
below:
95 86 105 89 89 99 78 110 113 87 77 96 103 115 86 95 94 106 99 99 83 76 94 99 102
99 104 93 101 94
(i) Organize the data into stem-and-leaf display
(ii) Around what values does the price of the spare part tend to cluster?
(iii) What is the most commonly quoted price? (6 marks)
(b) Consider the following set of scores of a sample:
5, 8, 12, 10, 15, 18, 21, 24, 7, 18, 10, 6, 4, 11, 15, 9, 22, 10
(i) Determine the mean and the standard deviation
(ii) Form a cumulative frequency distribution
(iii) Construct an ogive
(iv) Find the value of x for which the data set will divided into two-equal halves
(6 marks)
(c) The density function for a continuous random function X is given by
ïî
ïí
ì £ £
=
otherwise
x x
f x
0,
, 0 2
( ) 2
Find (i) find the mean of the distribution
(ii) Find the variance and standard deviation
(iii) P (1/2 = x =1)
(iv) P (1 =x) (6 marks)
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