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An 800 page book has 400 misprints. If the misprints are distributed uniformly throughout the book and the Poisson approximation to the binomial distribution is used to calculate the probability of exactly 2 misprints on page 16, which of the following represents the correct use of the Poisson approximation?

$\frac{e^{-0.5}}{8}$

Answer: $\frac {e^{-0.5}}{0.8}$

Solution:-

Given, an 800 page book has 400 misprints. Therefore average rate $\lambda = 400/800 = 0.5$ misprints per page

If X follows poisson distribution, then $P(X = x) = \frac{e^{-\lambda} * \lambda^x}{x!}$, $x = 0,1,2..$

Probability of exactly 2 misprints on page 16 = $P(X=2)$

$= \frac {e^{-0.5}*(0.5)^2}{2!} = \frac {e^{-0.5}}{0.8}$ (Answer)

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