 Probability

# Poisson Distribution

Passengers drop by a busy store at an average rate of $\lambda = 4$ per minute. If the number of passengers dropping by the store obeys a Poisson distribution, what is the approximate probability that $16$ passengers drop by the store in a particular $4$ minute period?

If a random variable $X$ obeys the Poisson distribution with mean $2,$ what is its variance $\text{Var}(X)?$

Assume that bacteria of a species called $X$ are randomly distributed in a certain river $Y$ according to the Poisson distribution with an average concentration of $16$ per $40 \text{ ml}$ of water. If we draw $10 \text{ ml}$ of water from the river using a test tube, what is the approximate probability that the number of bacteria $X$ in the sample is exactly $4?$

According to the maintenance department of a university, the number of toilet blockages obeys a Poisson distribution with an average of $6$ failures everyday. Then what is the approximate probability that there will be $4$ failures during a particular day? Which of the following is the correct graph for the probability distribution of a random variable $X$ that follows the Poisson distribution with mean $10?$

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