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Dit 401 Probability And Statistics Question Paper
Dit 401 Probability And Statistics
Course:Diploma In Information Technology
Institution: Kca University question papers
Exam Year:2014
UNIVERSITY EXAMINATIONS: 2013/2014
ORDINARY EXAMINATION FOR THE DIPLOMA IN
INFORMATION TECHNOLOGY
DIT 401 PROBABILITY AND STATISTICS
DATE: AUGUST, 2014
TIME: 11/2HOURS
INSTRUCTIONS: Answer Any Three Questions
QUESTION ONE
a) Distinguish between mutually exclusive and independent events
(4 Marks)
b) 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. (4 Marks)
c) There are 24 elephants in a game reserve. The warden tags 6 of the elephants with
small radio transmitters and returns them to the reserve. The next month, he
randomly selects 5 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)
d) The mean and standard deviation of 20 items was found to be 10 and 2 .Later on it
was discovered that the item 12 was misread as 8.Calculate the correct mean and
standard deviation.
(6 Marks)
1
QUESTION TWO
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.
(4 Marks)
ii. calculate Pearson’s correlation coefficient correct the answer to four decimal
places.
iii.
(10 Marks)
calculate the rank correlation coefficient correct to four decimal places.
(6 Marks)
QUESTION THREE
a) In a school, 60% of the pupils have access to the internet at home. A group of 8
students is chosen at random. Find the probability that
i. exactly 5 have access to the internet. (3 Marks)
ii. at least 6 students 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 under 25 5
25 but under 30 10
30 but under 35 25
35 but under 40 35
40 but under 45 25
45 but under 50 5
i. Calculate the mean and standard deviation.
ii. Calculate the Karl Pearson’s measure of skewness and comment on it.
(13 Marks)
2
QUESTION FOUR
a) Distinguish between correlation and regression.
(4 Marks)
b) If a random variable X follows a Poisson distribution such that
PX
1
PX
2
.Find
i. P X 0 (3 Marks)
ii. P X 2 (4 Marks)
c) From the following data of the heights (in inches) of a group of plants.
6.1, 6.2, 6.2, 6.3, 6.1, 6.4, 6.4, 6.0, 6.5, 6.3, 6.4, 6.5, 6.6, 6.4, 6.3
Calculate
i. Mode (1 Mark)
ii. Median (2 Marks)
iii. semi interquartile range (2 Marks)
iv. coefficient of variation (4 Marks)
QUESTION FIVE
a) In an examination 30% of the students have failed in DIT 304 , 20% of the
students have failed in DIT 305 and 10% have failed in both DIT 304 and
DIT 305 .A student is selected at random.
i.
what is the probability that the student has failed in DIT 304 when it is
known that he has failed in DIT 305 .
ii.
(4 Marks)
what is the probability that the student has failed either in DIT 304 or in
(4 Marks)
DIT305.
iii.
what is the probability that the student has failed in both DIT304 and
DIT305 .
(3 Marks)
b) Given the bivariate data
X: 1 5 3 2 1 1 7 3
Y: 6 1 0 0 1 2 1 5
Fit a regression line of Y on X and hence predict Y when x = 10. (9 Marks)
3
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