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Summer 2016 PROGRAM- MCA(REVISED
FALL 2012)
SEMESTER- FOURTH
SUBJECT CODE & NAME- MCA4020- PROBABILITY AND
STATISTICS
Q1. Three
machines A, B and C produce respectively 60%, 30% and 10% of the total number of items of a factory. The percentage of
defective output of these machines are respectively 2%, 3% and 4%. An item is
selected at random and is found to be defective. Find the probability that the
item was produced by machine C.
Solution: Let P(A), P(B) and P(C) denote the
probabilities of choosing an item produced by A, B, C respectively.
Also, let P(X/A), P(X/B), P(X/C) denote the
Q3. The data shows the
distribution of weight of students of 1st standard of a school. Find
the quartiles.
|
Class Interval
|
13 - 18
|
18 - 20
|
20 - 21
|
21 – 22
|
22 - 23
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23 - 25
|
25 – 30
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Frequency
|
22
|
27
|
51
|
42
|
32
|
|
16
|
10
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Solution:
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Q4. Fit a trend line to the
following data by the freehand method:
|
Year
|
Production of wheat
|
Year
|
Production of wheat
|
|
|
(in tonnes)
|
|
(in tonnes)
|
|
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1995
|
20
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2000
|
25
|
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1996
|
22
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2001
|
23
|
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1997
|
24
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2002
|
26
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1998
|
21
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2003
|
25
|
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1999
|
23
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2004
|
24
|
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|
Solution:
Graphical
representation of trend line relating to the production of wheat by the
method of free hand curve is shown in figure
Q5. Let X be a random variable and its
probability mass function is 
find the m.g.f. of
X and hence its mean and variance.
find the m.g.f. of
X and hence its mean and variance.
Solution: By definition,
Q6.
The
diastolic blood pressures of men are distributed as shown in table. Find
the standard deviation and variance.
|
Pressure(men)
|
78-80
|
80-82
|
82-84
|
84-86
|
86-88
|
88-90
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No. of
Men
|
3
|
15
|
26
|
23
|
9
|
4
|
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|
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|
|
Solution:
The table
represents the frequency distribution of data required for
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