The number of persons joining a cinema ticket counter in a minute follows a Poisson distribution with…

The number of persons joining a cinema ticket counter in a minute follows a Poisson distribution with parameter 6, then the probability that at least one and at most five persons join the queue in a particular minute is
  1. $\mathrm{e}^{-6 \times 6}(25.48)$
  2. $e^{-6}\left(\frac{6}{2}+\frac{6^3}{3 !}+\frac{6^4}{4 !}\right)$
  3. $6 \times \mathrm{e}^{-6}(29.8)$
  4. $e^{-6}\left(6+\frac{6^2}{2}+\frac{6^3}{3 !}+\frac{6^4}{4 !}\right)$

Solution

(c) We have Poisson distribution $ \begin{aligned} & P(X)=\frac{e^{-\lambda} \lambda^x}{x !} \text { where } \lambda=6 \\ & \therefore P(1 \leq x \leq 5)=e^{-6}\left[\frac{6^1}{1}+\frac{6^2}{2 !}+\frac{6^3}{3 !}+\frac{6^4}{4 !}+\frac{6^5}{5 !}\right] \\ & =e^{-6} \cdot 6(1+3+6+9+10.8)=6 . e^{-6}(29.8) \end{aligned} $

Asked in: AP EAMCET 2023 (19 May Shift 1)

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