The number of rainy days per month at Seattle follows a Poisson distribution with a mean value of 4.5 days.What is the probability that it will rain 3 days next month?
A)0.3604
B)0.2222
C)0.1687
D)0.2521

Question

Quizplus · Accepted Answer

The probability of observing $k$ events (in this case, rainy days) in a fixed interval of time or space when these events occur with a known constant mean rate ($\lambda$) and independently of the time since the last event, follows the Poisson distribution formula: $P(k; \lambda) = \frac{\lambda^k e^{-\lambda}}{k!}$. Here, $\lambda = 4.5$ (the mean number of rainy days per month) and $k = 3$ (the number of rainy days we're calculating the probability for). Plugging these values into the formula gives: $P(3; 4.5) = \frac{4.5^3 e^{-4.5}}{3!} = 0.1687$.

The Number of Rainy Days Per Month at Seattle Follows