UNIVERSITY EXAMINATIONS: 2010/2011
FIRST YEAR EXAMINATION FOR THE DEGREE OF BACHELOR OF
SCIENCE IN INFORMATION TECHNOLOGY
BIT 1301: PROBABILTY AND STATISTICS
DATE: AUGUST 2011 TIME: 2 HOURS
INSTRUCTIONS: Answer question ONE and any other TWO questions
Question One
a) Define the following terms as used in probability and statistics:
i) Set
ii) Sample Space
iii)Probability
iv)Statistics
v) Correlation
vi)Skewness
vii) Kurtosis
viii)Mutually Exclusive Event (8 Marks)
b) A newspaper vendor receives 600 newspapers daily as follows; 200 copies of newspaper A, 150
copies of newspaper B and 250 copies of newspaper C. On a particular day, 75% of A, 82% of B
and 90% of C have prospects randomly inserted inside the paper.
i) What is the probability that the first customer of the day receives a newspaper without a
prospect? (3 Marks)
ii) Suppose the customer received a newspaper with a prospect, what is the probability that he
bought newspaper B? (3 Marks)
c) A discrete random variable X has a probability distribution as given below:
(5 Marks)
Question Two
The following table shows the distribution of marks of 40 students in a statistics examination.
marks 0-10` 10-20 20-30 30-40 40-50
frequency 4 12 15 3 6
Calculate the:
i) Average mark (4 Marks)
ii)Mode (3 Marks)
iii) Median (3 Marks)
iv) Standard deviation (4 Marks)
v)First coefficient of skewness and comment (3 Marks)
vi) Moment coefficient of Kurtosis (3 Marks)
Question Three
(8 Marks)
b) In a large flower farm 20% of a particular kind of flower is red and the remaining 80% is white. The
farmer decides to take a sample of the flowers from the production. What is the probability that he
obtains
i) One or two red flowers in a sample of two
ii) At least two red flowers in a sample of three
iii)At most two red flowers in a sample of three. (9 Marks)
c) A card is drawn at random from an ordinary deck of 52 playing cards. Find the probability that the
card drawn is a 10 or a spade. (3 Marks)
Question Four
a) In a class of 100 students, 32 students study psychology, 38 students study sociology and 30
students study philosophy. The end of semester summary was as follows: Average mark for
Psychology is 68 Marks with a standard deviation of 5 marks, Average Mark for sociology was
80% with a standard deviation of 3 Marks, Average Mark for philosophy was 60% with a standard
deviation of 4 marks.
Calculate the mean and the standard deviation of the whole class. (10 Marks)
b) Two events A and B are mutually exclusive. Copy and complete the contingency table below and
hence determine
(10 Marks)
Question Five
The mileage Y that can be covered with a litre of a certain brand of gasoline depends on the amounts X
of a certain chemical additive in the gasoline. The following were results from 10 pairs of
observations X and Y.
i) Determine the product moment correlation coefficient and coefficient of determination between
X and Y. Comment on your answer. (10 Marks)
ii) Use the method of least squares to fit a regression line that can be used to predict mileage Y
given the amount of chemical additive X in the gasoline. (8 Marks)
iii)Estimate the mileage Y given that the amount of additive is 0.35. (2 Marks)
