GATE (TF) Textile 2012 Question Paper Solution | GATE/2012/TF/34

Question 34 (Textile Engineering & Fibre Science)

The number of neps in a carded web follows Poisson distribution with a mean of 100 per m². The probability that there is no nep in an area of 645 cm² is

(A)	$e^{-6.45}$
(B)	$e^{6.45}$
(C)	$e^{-645}$
(D)	$e^{645}$

Answer / Solution

By Poisson distribution-
Mean=100 per m2
Then no. of neps=?
Probability that there is no neps in an area 645 cm2=?
By Poisson distribution-
= $\frac{e^{-m} \times m^r}{r!}$
= $\frac{e^{-m} \times m^r}{r!}$
= $e^{-645/100}$
= $e^{-6.45}$ Ans
Option A is correct.

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