UNIVERSITY EXAMINATIONS: 2013/2014
ORDINARY EXAMINATION FOR THE BACHELOR OF SCIENCE
IN INFORMATION TECHNOLOGY/BUSINESS INFORMATION
TECHNOLOGY
BIT1301 BUSS 202 PROBABILITY AND STATISTICS
DATE: AUGUST, 2014 TIME: 2 HOURS
INSTRUCTIONS: Answer Question ONE and any other TWO
QUESTION ONE (30 Marks)
a) The grades of a group of1000students in an exam are normally distributed with amean of70and standard deviation of10. A student from this group is selectedrandomly.
i) Find the probability that his or her grade is greater than
80. (3 Marks)
ii) Find the probability that his or her grade is less than
50. (3 Marks)
iii) Find the probability that his or her grade is between50and80.
(3 Marks)
iv) Approximately ,how many students have grades greater than
80.
(2 Marks)
b) There are24elephants in a game reserve. The warden tags6of the elephantswith small radio transmitters and returns them to the reserve. The next month, herandomly selects5
elephants from the reserve. He counts how many of these
elephants are tagged. Assume that no elephants leave or enter the reserve or die
or give birth, between the tagging and the selection; and that all the outcomes of
the selection are equally likely. Find the probability that exactly two of the
selected elephants are tagged, giving your answer correct to three decimal places.
(4 Marks)
c) Let a random variable
X
have probability density function.
X 0 1 2 3 4
P X x 0.08 0.15 0.45 0.27 0.05
Compute:
i) Expected value of X
ii) Standard deviation of X (6 Marks)
d) Distinguish between binomial distribution and Poisson distribution. (4 Marks)
e) On average one in
200
computers break down in a certain fir per day. Find the
probability that out of a sample of
200
computers selected at random:
i) None breaks down (2 Marks)
ii) More than two breaks breakdown. (3 Marks)
QUESTION TWO (20 Marks)
a) In a school,60%of the pupils have access to the internet at home. A group of8students is chosen at random. Find the probability that
i) exactly
5
have access to the internet. (2 Marks)
ii) at least6students have access to the internet. (4 Marks)
b) The following set of data represents the distribution of annual salaries of a random
sample of
100
managers in a large multinational company:
Salary Range ($’000’) Managers
20
but under25 525but under30 10 30but under35 25 35but under40 35 40but under45 25 45but under50 5
i) Calculate the mean and standard deviation. (7 Marks)
ii) Calculate the Karl Pearson’s measure of skewness and comment on it.
(4 Marks)
iii) Calculate
95%confidence level for the annual mean salaries. (3 Marks)
QUESTION THREE (20 Marks)
a) Distinguish between correlation and regression. (4 Marks)
b) The Marks scored by students in a mathematics and science tests were as shown in
the table below.
Students
A B C D E F G H I J
Mathematics
89 75 68 74 82 63 66 79 80 58
Science
85 77 74 72 80 68 62 78 83 59
i) Draw a scatter diagram of this data. (3 Marks)
ii) Calculate Pearson’s correlation coefficient correct the answer to four decimal
places. (7 Marks)
iii) Calculate the rank correlation coefficient correct to four decimal places.
(6 Marks)
QUESTION FOUR (20 Marks)
a) In a school,
60%of the pupils have access to the internet at home. A group of8
students is chosen at random. Find the probability that
i) Exactly5
have access to the internet. (2 Marks)
ii) At least6
students have access to the internet. (3 Marks)
b) The probability that a driver stopping at a petrol station will have his car tyres
checked is
0.012
, the probability that he will have both oil checked is
0.29and the
probability that he will have both oil and tyres checked is
0.07
.What is the
probability that a driver stopping at this station will have neither his car tyres checked
nor oil? (4 Marks)
c) The Marks of800candidates in an examination were normally distributed with meanof
Marks and the standard deviation of20Marks. If5%of the candidatesobtained a distinction by scoring
X
Marks or more, estimate the value of
X.
(5 Marks)
d) A bag contains6white and9black balls. Two drawings of4
balls are made suchthat (a) the balls are replaced before the second trial (b) the balls are not replaced4
before the second trial. Find the probability that the first drawing will give4black
balls in each case. (6 Marks)
QUESTION FIVE (20 Marks)
a) IfP A 0.5, P B 0.3
andP A B 0.2
, obtain the probability that
i)
A occurs but not
B . (3 Marks)
ii) At least one of
A
and
B
occurs. (3 Marks)
iii) Neither of
A
and
B
occurs. (2 Marks)
b) The table below shows test scores and sales for various salespersons. Use it to
answer the questions that follow.
Salesperson 1 2 3 4 5 6 7 8 9 10
Testscore 44 65 50 57 96 94 110 34 79 65
Sales (Ksh ‘000’) 41 60 40 50 80 68 84 70 55 48
i) Using the least square method, determine the regression equation for sales on
testscore. (10 Marks)
ii) Estimate the weekly sales given that a salesperson makes a testscore of 100.
(2 Marks)
