**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)