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Probability And Statistics Question Paper

Probability And Statistics

Course:Diploma In Information Technology

Institution: Kca University question papers

Exam Year:2010

UNIVERSITY EXAMINATIONS: 2008/2009
STAGE IV EXAMINATION FOR DIPLOMA IN INFORMATION
TECHNOLOGY
DIT 401: PROBABILITY AND STATISTICS
DATE: APRIL 2010 TIME: 1½HOURS
INSTRUCTIONS: Answer any THREE questions
Question One
a) given that the mean of the following data is X
42, 36, 38, X-25, 51, 38, X, 43
Find ;
i) value of X
ii) MAD
iii) Variance of the data
iv) Lower quartile and upper quartile
v) 50th percentile
vi) 8th decile (12 Marks)
b) Differentiate between not mutually exclusive events and independent events (2 Marks)
c) Describe any THREE diagrammatic representations of data (6 Marks)
Question Two
a) Briefly describe the steps involved in statistics study (4 Marks)
b) The table below gives the probability distribution frequency of a random variable X.
2
Given that the mean of X is 1.375, find the values of p and q (6 Marks)
c) Calculate the mean from the following frequency distribution using the Assumed Mean method
WAGES NO. OF WORKERS
300-319 15
320-339 27
340-359 38
360-379 43
380-399 22
400-419 17
420-439 9
440-459 4
(8 Marks)
Question Three
a) A research on a certain variable came up with the frequency distribution table below
Calculate
i) mean
ii) median (8 Marks)
b) Describe any THREE measures of central tendency (3 Marks)
c) A bag contains 7 red balls and 5 white balls.4 balls are drawn at random.What is the probability
that
i) all of them are red
ii) two of them are red and two of them are white (5 Marks)
d) Differentiate between the term statistics and probability (2 Marks)
Question Four
a) Define the following terms
X 0 1 2 3
P(x) p 2q p + q q
Class intervals frequency
60-63 8
63-66 28
66-69 118
69-72 66
72-75 16
75-78 8
3
i. skewness
ii. kurtosis
iii. sampling
iv.census (8 Marks)
b) There are 3 baskets labeled A, B and C. Basket A contains 4 ripe mangoes and 2 unripe ones and
basket B contains 3 ripe mangoes and 2 unripe ones. Basket C contains 2 ripe mangoes and 3
unripe ones. If two mangoes are picked at random from any of the baskets without replacement,
draw a tree diagram to represent this information and hence, find the probability of picking
i. draw a probability tree (2 Marks)
ii.Two ripe ones (2 Marks)
iii.No ripe ones (2 Marks)
c) Assuming a poisson distributed event had a mean of 1.72 within some given interval,let x be the
number of occurrence of an event, state the poisson equation hence use it to calculate when
i)x=0
ii)x<=2 (6 Marks)
Question Five
a) Discuss any four measures of variation (4 Marks)
b) A box contains two black tops three white tops and four red tops . What is the probability that if
one top is taken out its
i. black
ii. white
iii.Not red (6 Marks)
c) A deck of 52 cards has 13 spades . If two cards are drawn from the deck at random, what is the
chance that both are spades (4 Marks)
d) Twenty five patients were given a blood test to determine their blood types
A,B,B,AB,O,O,O,B,AB,B,B,B,O,A,O,AB,O,O,O,AB,A,A,O,B,A create a frequency distribution hence
create a chart for the data (6 Marks)

Probability And Statistics Question Paper

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