Question

The number of gamma rays emitted per second by a certain
radioactive substance is a random variable having Poisson distribution
with
  5.8. If a recording instrument becomes inoperative when
there are more than 12 rays per second, what is the probability that this
instrument becomes inoperative during any given secondHa 4

Answer 1

Question #68505, Math / Statistics and Probability

The number of gamma rays emitted per second by a certain radioactive substance is a random variable having Poisson distribution with $\lambda = 5.8$. If a recording instrument becomes inoperative when there are more than 12 rays per second, what is the probability that this instrument becomes inoperative during any given second.

Answer.

$$\mathbf{P}(\mathbf{X} > \mathbf{12}) = \mathbf{1} - \mathbf{P}(\mathbf{X} \leq \mathbf{11}) = \mathbf{1} - \mathbf{e}^{-\lambda} \sum_{\mathbf{n}=0}^{11} \frac{\lambda^{\mathbf{n}}}{\mathbf{n}!} = \mathbf{1} - \mathbf{e}^{-5.8} \sum_{\mathbf{n}=0}^{11} \frac{5.8^{\mathbf{n}}}{\mathbf{n}!} = 0.0068.$$

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