Probability And Statistics Question Paper
Probability And Statistics
Course:Bachelor Of Science In Information Technology
Institution: Kca University question papers
Exam Year:2011
UNIVERSITY EXAMINATIONS: 2010/2011
FIRST YEAR EXAMINATION FOR THE DEGREE OF BACHELOR OF
SCIENCE IN INFORMATION TECHNOLOGY
BIT 1301: PROBABILITY AND STATISTICS
DATE: APRIL 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) Random Variable
ii) Event
iii) Statistics
iv) Probability
v) Skewness
vi) Mutually Exclusive event (6 Marks)
b) Events A and B are mutually exclusive. Complete the contingency table below and use it to
calculate the following probabilities:
i) P(A/B)
ii) P( AC U BC)
A AC
B 1
5
Bc 4
7
(5 Marks)
c) Suppose a random variable X takes on the values -3, -1, 2 and 5 with respective probabilities
2
2 3
10
k -
, 2
10
k -
, 1
10
k -
, 1
10
k +
i) Determine the probability distribution of X (5 Marks)
ii) Find the expected value E(X) of X. (2 Marks)
d) Suppose 2% of items produced in a factory are defective. Find the probability that there are 3
defective items in a sample of 100 items. (3 Marks)
e) Consider the following data where X denotes the ages of 6 children and Y denotes the
corresponding number of correct answers in a 10 question test:
X 5 6 6 7 7 8
Y 6 6 7 8 9 9
Calculate the correlation coefficient for the data set and comment. (6 Marks)
f) Suppose A and B are events with P(A)=0.6, P(B)=0.3 and P(A n B)=0.2 Find the probability that
i) A does not occur
ii) B does not occur
iii) A or B occurs (3 Marks)
QUESTION TWO
a) A dice is weighted so that the outcomes produce the following probability distribution:
Outcome 1 2 3 4 5 6
Probability 0.1 0.3 0.2 0.1 0.1 0.2
Consider the events:
A={Even Number}, B={2,3,4,5}, C={x: x<3}, D={x: x>7}
Find the following probabilities:
i) P(A) (1 Mark)
ii) P(B) (1 Mark)
iii) P(C) (1 Mark)
iv) P(D) (1 Mark)
v) P(A nB) (1 Mark)
vi) P(A ?C) (1 Mark)
vii) P(B nC) (1 Mark)
3
b) 100 students pursuing a course in IT were examined and their results were summarized as
shown in the table below:
Marks Number of students
20 – 24
25 – 39
40 – 49
50 – 54
55 – 69
70 – 79
10
20
25
15
20
10
Calculate the:
i) Average mark (4 Marks)
ii) Median mark (2 Marks)
iii) Most occurring mark among the students (2 Marks)
iv) Standard deviation (5 Marks)
QUESTION THREE
a) The probability that A hits a target is 1
4
, and the probability that B hits the target is 2
5
. Both shoot
at the target. Find the probability that at least one of them hits the target. (4 Marks)
b) Consider the following frequency distribution which gives the number f of students who got x
correct answers on a 20-question exam:
x 9 10 12 13 14 15 16 17 18 19 20
f 1 2 1 2 7 2 1 7 2 6 4
i) display the data in a histogram and frequency polygon (6 Marks)
ii) Calculate the mean, variance and standard deviation of the data. (10 Marks)
QUESTION FOUR
a) A class of IT students sat calculus and linear algebra papers in the December 2009 examination.
The Marks obtained by the candidates were as follows:
Calculus 8 12 21 34 36 42 43 53 54 58 70 83
Linear
algebra
20 15 18 22 41 42 50 43 54 62 70 85
i) Draw a scatter diagram to show the above scenario. (2 Marks)
ii) Determine the rank correlation coefficient and comment on its value. (8 Marks)
4
b) A college in Nanyuki concists of 40% first years of whom 15% are Nairobi residents, 25% second
years of whom 40% are Nairobi resident, 20% third years of whom 25% are Nairobi residents and
15% fourth years of whom 20% are Nairobi residents. A student is randomly selected from this
college:
i) Find the probability that the student is a Nairobi resident (4 Marks)
ii) If the student is a Nairobi resident, find the probability that the student is
• First year (3 Marks)
• Third year (3 Marks)
QUESTION FIVE
a) The probability density function of the random variable X is given by
( 1) 2 4
( )
0
k x for x
f x
elsewhere
? + < <
=??
Find
i) the value k (3 Marks)
ii) P(X< 3.2) (3 Marks)
iii) The mean of X (4 Marks)
b) The yearly rainfall, measured to the nearest tenth of a centimeter, for a 30 year period follows:
42.3, 35.7, 47.5, 31.2, 28.3, 37.0, 41.3, 32.4, 41.3, 29.3
34.3, 35.2, 43.0, 36.3, 35.7, 41.5, 43.2, 30.7, 38.4, 46.5
43.2, 31.7, 36.8, 43.6, 45.2, 32.8, 30.7, 36.2, 34.7, 35.3
i) Construct the frequency distribution table where the data is grouped into 10 classes 28-
30, 30-32, 32-34,. . . ., 46-48. (4 Marks)
ii) Calculate the mean and median of the data. (6 Marks)
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