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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:2010

STRATHMORE UNIVERSITY
BACHELOR OF COMMERCE
END OF SEMESTER EXAMINATION
MAT: 2101: INTRODUCTION TO BUSINESS STATISTICS
DATE: TIME:
INSTRUCTIONS
The Question paper consists of Five questions. Answer Question one and any other two
questions.
Question one
(a) i.) Compare descriptive and inferential statistics, and give an example of
each. (2 marks)
ii.) A teacher wishes to know whether the males in a certain institution have
more favorable interests in soccer than do the females. All students in
his/her class are given a questionnaire about soccer and the mean
responses of the males and the females are compared. Is this an example
of descriptive or inferential statistics give reasons? (2 marks)
(b) Indicate whether each of the following statements is TRUE or
FALSE. If FALSE, what is required to make the statement TRUE.
i) If two events, A and B, are mutually exclusive , then
P(A or B) = P(A) + P(B)
ii) If A and B are two events, then
P(A and B) = P(A)P(B)
no matter what relation there is between A and B
iii) The probability distribution function of a discrete random variable
cannot have a value greater than 1
iv) The probability that a continuous random variable lies in the interval
3 to 6, inclusive, is the sum of P(3) + P(4) + P(5) + P(6)
v) The standard normal distribution has a mean zero and standard
deviation s (5 marks)
(b) In a survey of 200 companies, 120 contracted for outside pension plans for their
employees, 50 had their own pension funds, and 30 had a combination plan.
Construct a percentage frequency bar chart for these pension plans. (5 marks)
(c) Find the expected number of breakdowns in a week for a certain printer if the
probability of no breakdowns in a week is 0.30, the probability of one breakdown
is 0.60, and the probability of two breakdowns is 0.10. What is the standard
deviation of the breakdowns for this printer? (6 marks)
(d) From 4 red, 5 green and 6 yellow apples, how many selections of 9 apples are
possible if 3 of each color are to be selected? (4 marks)
(e) One bag contains 4 white and 2 black balls. Another bag contains 3 white and 5
black balls. If one ball is drawn from each bag, find the probability that
i.) both are white
ii.) both are black
iii.) one is white and one is black. (6 marks)
Total (30 marks)
Question two
(a) Every night a hotel has a number of people who book rooms by telephone, but do
not actually turn up. The number of no-shows was recorded over a typical period
as follows:
4 2 6 7 1 3 3 5 4 1 2 3 4 3 5 6 2 4 3 2 5 5
0 3 3 2 1 4 4 4 3 1 3 6 3 4 2 5 3 2 4 2 5 3 4
i) Prepare a table showing the corresponding data set against frequency;
(2 marks)
ii) Draw a percentage cumulative frequency curve for the data set (3 marks)
iii) What is the probability that there are more than four no-shows on any
day. (2 marks)
(b) If X is a random variable representing the number of magazines sold daily by a
street vendor and whose probability distribution is given by
x 0 2 4 6 8 10
f(x) 0.1 0.2 0.3 0.2 0.1 0.1
i.) Find the expected daily sales for the street vendor (3 marks)
ii.) What is the standard deviation of daily sales for this vendor? (4 marks)
iii.) Find the probability that the Vendor will sell more than 4 magazines in
one day (2 marks)
iv.) Suppose that the street vendor receives a fixed daily payment of Shs.
10,000 from the book store and Shs. 50.00 for every magazine he sells.
What is the street vendors expected daily income and it’s standard
deviation? (4 marks)
Total (20 marks)
Question Three
A manufacturer of photographic devices is conducting a survey of the claims received by
the customers regarding one of its digital cameras. The claims are classified by their
nature (problem with the lens, problem with the battery, or any other type of problems)
and by their timing (before or after the end of the guarantee period of the camera). The
table below presents the number of claims in each category:
i.) What is the probability that the customer’s claim is related to the lens?
(1 mark)
ii.) What is the probability that the customer’s claim is received after guarantee
period has expired? (1 mark)
iii.) What is the probability that the claim is related to the battery and is received
during the guarantee period? (2 marks)
iv.) What is the probability that a claim is related to other problems or it is
received after guarantee period has expired? (2 marks)
v.) Suppose that a claim received is related to the lens, what is the probability it
is received after guarantee period has expired? (3 marks)
vi.) Suppose a claim is received during the guarantee period, what is the
probability it is related to the battery? (3 marks)
vii.) Are the events of a claim being related to the lens and claim being issued
during the guarantee period statistically independent? (3 marks)
(b) Among the 78 doctors on the staff of a hospital, 64 carry malpractice insurance, 36
are surgeons, and 34 of the surgeons carry malpractice insurance. If one of these
doctors is selected at random to represent the hospital staff at a convention, what is
the probability that the one selected is not a surgeon and does not carry malpractice
insurance? (5 marks)
Total (20 marks)
Question Four
(a) A certain computer has two power supplies. The computer can operate on either
one. On any given day, the first is 99% reliable and the second is 99.5% reliable.
i.) What is the probability that on any given day the computer will
lose its power? (3 marks)
ii.) What is the probability that on any given day the computer will
operate on one power supply? (3 marks)
(b) Suppose that 20% of all flights at a particular airport experience delays. If an
executive takes 10 flights from the airport next month, find the probability that at
least 5 of the flights will be delayed (4 marks)
(c) Suppose that a production facility experiences an average of 3 accidents per week.
Find the probability that in a particular week exactly 5 accidents will occur.
(4 marks)
(d) A group of 10 boys and 10 girls is divided into two equal groups.
i.) Find the probability that each group has equal number of boys and
girls. (3 marks)
ii.) Find the probability that one group has 6 boys (3 marks)
Total (20 marks)
Question Five
Telephone calls put on hold have mean length 55 seconds and standard deviation 15
seconds. If the distribution of holding times is bell-shaped,
i.) Find the z-score for a call that was put on hold for 82 seconds.
(1 mark)
ii.) Is an 82 second wait unusual? Why? (1 mark)
iii.) What holding time would correspond to the standard score of
2
5
Z = ? (2 marks)
iv.) What percentage of calls are put on hold for less than 25 seconds?
(3 marks)
v.) What can you say about calls that are on hold for more than 100
seconds? (2 marks)
vi.) What is the probability that a certain call will be put on hold for
more than 70 seconds (3 marks)
vii.) What is the probability that a certain call will be put on hold for
less than 10 seconds (3 marks)
viii.) What is the probability that a certain call will be put on hold for
less than 25 seconds or more than 85 seconds? (3 marks)
ix.) What is the probability that a certain call will be put on hold
between 40 seconds and 70 seconds ? (2 marks)
Total (20 marks)

Introduction To Business Statistics Question Paper

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