Question

Situation D: Suppose that, in a one-minute period during an electrical storm, the number of lightning strikes on a radar antenna follows a Poisson distribution with a mean of 2.40. Question D1: Find the probability that the antenna will be struck exactly once during this time period.

Answer 1

Answer:

21.77% probability that the antenna will be struck exactly once during this time period.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

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

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

In this question:

$\mu = 2.40$

Find the probability that the antenna will be struck exactly once during this time period.

This is P(X = 1).

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

$P(X = 1) = \frac{e^{-2.40}*2.40^{1}}{(1)!} = 0.2177$

21.77% probability that the antenna will be struck exactly once during this time period.