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Principles Of Marketing Question Paper
Principles Of Marketing
Course:Bachelor Of Commerce
Institution: Strathmore University question papers
Exam Year:2006
STRATHMORE UNIVERSITY
FACULTY OF COMMERCE
Bachelor of Commerce
END OF SEMESTER EXAMINATION
MAT: 1103 INTRODUCTION TO BUSINESS STATISTICS
Date: 19th October 2006 Time:2 Hours
INSTRUCTIONS: ANSWER QUESTION ONE AND ANY OTHER TWO QUESTIONS.
QUESTION ONE (30 marks)
( a) Define the following terms (i) Inferential statistics (ii) Descriptive statistics
(6 marks)
(b) In a survey of a sample of interest rates on mortgages for 15-year mortgages at a local
lending banks was found to be: 7.1%, 7.3%, 7.0%, 6.9%, 6.6%, 6.9%, 6.5%, 7.3%, 6.8%
Calculate and interpret (i) the mean (ii) median (iii) mode (iv) variance (v) standard
deviation (6 marks)
( c) (i) Gogni Construction Company pays its hourly employees KSh. 65, 75 or 85 per
hour. There are 26 hourly employees; 14 are paid at 65 rate, 10 are paid at 75 and 2 are
paid at 85 rate.
Find the mean hourly rate paid to the employees. (2 marks)
(ii) Kamau’s Orchard sells apples in a large bag by weight. A sample of seven bags
contained the following numbers of apples: 23, 19, 26, 17, 21, 24 22. Compute the (i)
mean number of apples in a bag (ii) the median number of apples in a bag (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(Ac) (iii) P(Bc) (iv) P(AcnBc) (6 marks)
( e) Given the following discrete probability distribution
x: 0 1 2 3
p(x): 0.2 0.4 0.3 0.1
Compute (i) the mean (ii) variance (iii) standard deviation (4 marks)
( f) If the mean = 25 and standard deviation = 9, find (i) P(19 < X< 28)
(ii) P(X< 4) (2 marks)
2
QUESTION TWO (20 marks)
(a) Provide graphical illustration for the frequency distributions from which the following
measures of central tendency were derived. Describe the distributions in terms of
symmetry, indicating the directions of skewness of symmetric distribution:
mean = 46, median = 43, mode = 40,
mean = 43, median = 43, mode = 43
mean = 40 median = 43 mode = 46 (8 marks)
(b) The following is a frequency distribution of the selling prices of vehicles sold at
Kisumu Motors Ltd last month:
Selling prices (K£’000) Frequency
12 – 15 10
16 – 18 20
19 – 21 16
22 – 24 19
25 – 27 8
28 – 30 4
31 – 33 2
34 – 36 1
(i) Construct a histogram and a frequency polygon
(ii) Construct a cumulative frequency distribution
(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 p(x)
(8 marks)
( b) John Racho sells new cars for Baraka Motors ltd. John usually sells the larges
number of cars on Saturday. He has established the following probability distribution
for the number of cars he expects to sell on a particular Saturday:
No. of cars sold Probability, p(x)
0 0.10
1 0.20
2 0.30
3 0.30
4 0.10
3
Required: (i) What Type of distribution is this?
(ii) On a typical Saturday, how many cars should John expect to sell?
(ii) What is the variance and standard deviation of the distribution?
(6 marks)
( c) The yearly income for a group of 10,000 professionals is normally distributed with
mean = K£ 60,000 and standard deviation = K£5,000.
(i) What is the probability that a person from the group has a yearly income of
less than K£ 56,000?
(ii) How many of the people have yearly income of over K£70,000?
(6 marks)
QUESTION FOUR (20 marks)
( a) A sample of amount paid for car parking on Saturday in Thika town was
organized into the frequency distribution:
Amount paid Number of cars
30 – 75 2
75 – 100 7
100 – 125 15
125 – 150 28
150– 175 14
175– 200 9
200 – 225 3
225 – 250 2
Calculate (i) Range
(ii) mean amount paid
(iii) mean absolute deviation
(iv) variance and (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)
QUESTION FIVE (20 marks)
(a) Listed below is the number of 30-second radio advertisements sports purchased by
each of the 45 members of the Kenya Automobile Dealers Association last year:
96 93 88 117 127 95 113 96 139 142 94 197 125 155 155 103 112 135 132 111 125
104 106 139 118 136 125 143 120 103 113 124 108 94 146 156 112 127 117 120 134
119 97 89 138
4
(i) Organize the data into stem-and-leaf display
(ii) Around what values do the numbers of advertising sports tend to cluster?
(iii) What is the lowest and highest number of sports purchased by the dealers?
(6 marks)
(b) Consider the following set of scores of a sample:
24 18 20 28 15 25 24 12 26 18 14 20 24 17 16
Required:
(i) Determine the mean and the standard deviation
(ii) Convert each number to a standard score
(iii) Show that the set of standard scores has mean equal to zero and a standard
deviation equal to one.
(6 marks)
(c) The density function for a continuous random function X is given by
ïî
ïí ì
£ £
=
otherwise
kx x
f x
0,
, 0 2
( )
Find (i) k
(ii) P(1/2 = x =1)
(iii) P(1 =x ) (6 marks)
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