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If 6 is the mean of a poisson distribution, then $P (x \geq 3) =$

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$1 - \frac{25}{e^{6}}$

$e^{- 6} - 25$

$24 - 25 e^{6}$

$e^{- 3}$

answer is A.

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Detailed Solution

$P (X = x) = \frac{e^{- λ} λ^{x}}{x!}$

$λ = m e a n = 6$

$P (x \geq 3) = 1 - (P (x = 0) + P (x = 1) + P (x = 2))$

$= 1 - (\frac{e^{- 6} {.6}^{0}}{0!} + \frac{e^{- 6} {.6}^{1}}{1!} + \frac{e^{- 6} {.6}^{2}}{2!})$

$= 1 - \frac{1}{e^{6} (1 + 6 + 18)}$

$= 1 - \frac{25}{e^{6}}$

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