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Spring 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
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18 - 20
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20 - 21
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21 – 22
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22 - 23
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23 - 25
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25 – 30
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Frequency
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22
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27
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51
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42
|
32
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16
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10
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Solution:
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Class interval
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Frequency
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Cumulative frequency
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13
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– 18
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22
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22
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Q4. Fit a trend line to the
following data by the freehand method:
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Year
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Production of wheat
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Year
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Production of wheat
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(in tonnes)
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(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
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23
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1997
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24
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2002
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26
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1998
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21
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2003
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25
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1999
|
23
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2004
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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)
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78-80
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80-82
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82-84
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84-86
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86-88
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88-90
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No. of
Men
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3
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15
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26
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23
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9
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4
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Solution:
The table
represents the frequency distribution of data required for calculating
the standard
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