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Probability And Statistics I Question Paper
Probability And Statistics I
Course:Bachelor Of Science
Institution: Kenyatta University question papers
Exam Year:2010
KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2009/2010
INSTITUTIONAL BASED PROGRAMME (IBP)
EXAMINATION FOR THE DEGREE BACHELOR OF SCIENCE
SMA 160: PROBABILITY AND STATISTICS I
DATE:
Thursday 29th April 2010
TIME: 11.00a.m – 1.00p.m
INSTRUCTIONS: Answer Question one and any other two questions
Q1.
a)
Differentiate between the following terms
i)
Independent and dependent events
ii)
Mutually exclusive and mutually exhaustive events
iii)
Primary and Secondary sources of data
iv)
Continuous
and
discrete
variables
[8marks]
b)
A bag contains 5 red balls, 3 white balls and 7 blue balls. What is the
probability that a ball drawn at random will be,
i)
White
[1mark]
ii)
White or red
[2marks]
iii)
Neither
white
nor
blue [3marks]
c)
An incomplete distribution is given below
Variable 0-10 10-20 20-30 30-40 40-50
Frequency 14
f1 27 f2 15
If the median is 25 and the mode is 24 obtain the missing frequencies f1
and
f2.
Page 1 of 4
1
1
1
d)
Suppose
P( )
A = , P(B) =
and P(A n C) =
where A and C are
2
3
12
independent.
1
If P(B ? C) = show that B and C are mutually exclusive. [4marks]
2
e)
The first four moments of a distribution about the value 4 of a variable are
-1.5, 17,-30 and 108. Obtain the mean variance of the distribution.
[4marks]
f)
Given that the set (a, b, c ,d, e) has mean m and standard deviation s, write
down the mean and standard deviation of the set (a+k, b+k, d+k, e+k) in
terms of m and s respectively where k is a constant.
[2marks]
Q2.
Consider the following frequency distribution table.
Class
0-10
10-20 20-30 30-40 40-50 50-60
Interval
Frequency
15
17 19 27 19 12
a)
Find the mean and the standard deviation by changing both the location
(use an assumed mean of 35) and the scale (use common class width).
[7marks]
b)
Find
i)
Mode
ii)
Median
iii)
Interquartile
range
iv)
Coefficient
variation
v)
Coefficient
of
skewness
[13marks]
Q3.
a)
Out of 100 people, 25 are NARC, 35 are PNU and 40 are ODM
supporters. The percentage of NARC, PNU and ODM supporters who
read the Standard newspaper are 70%, 50% and 80% respectively.
Page 2 of 4
i)
If one person among the supporters is picked at random, what is
the
probability
the
he/she
reads the newspaper.
[2marks]
ii)
If one of the 100 people is observed reading The Standard, what is
the probability that he/she is an NARC supporter? [3marks]
b)
A and B are two events such that
1
P( )
A =
3
P A ? B =
3 and (
)
4 . Find
P(A | B where A | B = A n B if A and B are independent. [5marks]
c)
343 patients suffer from a certain disease. 96 of them were given a new
treatment and 14 of them cured. Of the untreated patients, 32 of them got
cured. If one patient is picked at random and is found to be cured, what is
the probability that he/se was not treated.
[5marks]
d)
A die is tossed four times. What is the probability that at least one’4’ will
occur.
[5marks]
Q4.
a)
The number of hours which ten students, taken in random, studied for an
examination are shown below.
No. of
8 6 11 13 10 5 18 15 2 9
hours
Grade in
56 44 79 72 70 54 94 85 33 65
examination
i)
Calculate the Spearman’s rank correlation coefficient.
[6marks]
ii)
What is the relationship between the number of hours studied and grade in
examination.
[2marks]
b)
The independent probabilities that the three sections X, Y and Z of a
costing department will encounter a computer error are: 0.1, 0.3, 0.3 each
week respectively. Determine the probability that:
i)
That there will be at least one computer error.
[3marks]
ii)
One and only one computer error will be encounter by the costing
department
next
week. [3marks]
Page 3 of 4
c)
The coefficient of rank correlation between marks in statistics and marks
in mathematics obtained by a certain group of students is 0.8, if the sum of
squares of the squares of the difference in ranks is given to be 13,
find the number of students in the group.
[6marks]
Q5.
Does the age at which a child begins to talk predict later score on a test of mental
ability? A study of the development of young children recorded the age in
months at which each of the 15 children spoke their first word and their Adaptive
Score, the result of an aptitude test taken much later. The data appear below.
Child 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Age 15 26 10 9 15 20 18 11 8 20 7 9 10 12 10
Score 95 71 82 91 102 87 93 100 104 94 113 96 83 84 102
i)
Plot a scatter diagram. What do you observe from the plot?
[4marks]
ii)
What is the correlation coefficient between the age and the Adaptive
scores?
[6marks]
iii)
Find the linear regression line that would predict the Adaptive score given
at any age.
[6marks]
iv)
Predict the score at age 19 and 21 months.
[4marks]
Page 4 of 4
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