Probability And Statistics I Question Paper

Probability And Statistics I

Course:Bachelor Of Science

Institution: Kenyatta University question papers

Exam Year:2009

KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2009/2010
FIRST SEMESTER EXAMINATION FOR THE DEGREE OF
BACHELOR OF SCIENCE

SMA 160: PROBABILITY AND STATISTICS I

DATE: Tuesday 22nd December, 2009
TIME: 2.00 p.m – 4.00 p.m

INSTRUCTIONS: Attempt Question ONE and any other TWO questions
Question ONE (30 Marks)

a)
Define the following terms
i)
Secondary
data
ii)
Kurtosis
likely
events
iii)
Equally likely events
iv)
Complementary events
v)
P(A/B)
b)
The following data shows the marks of 100 students

Marks 0-10 10-20 20-30 30-40 40-50 50-60
No. of
12 18 27 20 17 6
Students

i)

Draw
a
frequency
curve.
[3
marks]
ii)
Obtain
the
arithmetic
mean
[3
marks]
iii)
Calculate
the
median.
[3
marks]
iv)
Calculate
the
variance
[3
marks]

Page 1 of 3

c) A bag contains 3 green balls, 5 black and 7 yellow balls. What is the probability
that a ball drawn at random will be
i)
green

[1 mark]
ii)
black
or
green
[2
marks]
iii)
neither
green
nor
yellow
[2
marks]

Question TWO (20 marks)
a)
Given below is the distribution of candidates obtaining marks x or higher a certain
exam.
X 10 20 30 40 50 60 70 80 90 100
C.f 140 130 120 100 70 45 30 10 5 0

Obtain the ( i) mean (ii)
median (iii) mode of this distribution
b)
The following table shows an incomplete table.
Variable
10-20 20-30
30 - 40 40 -50
50-60
60-70
70-80
Frequency 12
30
f 1 65
f
2 25
18

Obtain the missing frequencies f 1 and f 2 if total is 229.

Questions THREE (20 marks)
a)
i)
Define the rth moment about a point.

[2 marks]

ii)
Define the rh moment about the mean.

iii)
The first four rth moment about the value 2 are 1, 16 and 40 .
Obtain the first three about the mean.

[6 marks]

b)
Below is a table of the height (in inches) of fathers (x) and their sons (Y).

X: 65
66
67
67 68
69 70
72
Y: 67
68
65
68 72
7 69
71

Page 2 of 3

i)
Find the least squares linear regression equation that could be used to predict the
height of a son given the height of a father .
ii)
Obtain the height of a son given that the father’s height is 71.

Question FOUR (20 marks)

a)
One black die and one green die are placed in a bag. One die is selected at
random and then rolled. It’s colour and number on the uppermost face are noted.
i)
Write down the sample space.

[4 marks]
ii)
Are all the events equally likely?

[2 marks]
iii)
What are the probability of the following events.
- green with any number

[2 marks]
- any colour with a six.

[3 marks]
- black with an odd number or green with an even number. [4 marks]
- neither black with an odd number nor green with an even number.

[5 marks]
Questions FIVE (20 marks)
In the Eva’s university college, 40% of the students are Science and 60% are Arts
students. Of the Arts students 65% are female. Of the Science students 20 % are female.
Some students live in the halls of residence. Of the male Science students 30% live in the
halls and of the male Art students 30 % live in the halls. The corresponding figures for
female students is 50%. Find the probability that a student chosen at random is
i)
a
female
student

[2
marks]
ii)
a
female
science
student.
[3
marks]

iii)
a science student given that the student is female.
[5 marks]
iv)
male and lives in the halls given the student is a Science student.

[5 marks]

v)
A science student given that the student is male lives in the halls.

[5 marks]

Page 3 of 3

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