in Mathematical Logic
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1 vote
1 vote

In this question if we do simply probability calculation then it is 8/20 40%

but when I am appling poisson distribution then it is 40.4%.

why we are getting two different answers??

in Mathematical Logic
516 views

4 Comments

poison distribution is used when avg probability of some event is given while binomial distribution is used when exact probabilty is given...
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thanks!!

but here I am using simple probability.
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how you got probability 0.4

I m getting 33/40  i.e 0.825

Total flaws(>3)/Total number of sheets
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in the question they are asking about 3 or more

No of sheets having flaws >= 3 / total no of sheets

8/20

40%
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1 Answer

2 votes
2 votes
$\lambda =\large ( \frac{4}{20} \times 0 ) + (  \frac{3}{20} \times 1)  + ( \frac{5}{20} \times 2 )+ ( \frac{2}{20} \times 3 ) + ( \frac{4}{20} \times 4) + (\frac{5}{20} \times 5  )+ (  \frac{1}{20} \times 6 ) = 2.3  $

$P\{X = i\} =  \Large \frac{e^{\lambda}\lambda^{i}}{i!}$

$P\{X = i + 1\} = P(i) \times  \Large \frac{\lambda}{i+1}$

$P\{X = 0\} =  \Large \frac{e^{-2.3}\times 2.3^{0}}{0!} = 0.100$

$P\{X = 1\} = P(0) \times  \Large \frac{2.3}{0+1} = 0.230$

$P\{X = 2\} = P(1) \times  \Large \frac{2.3}{1+1} = 0.264$

$P\{X > 2\} = 1 - 0.100 - 0.230 - 0.264 = 0.406$

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