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

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

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) = (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) = (e^(-\mu)*\mu^(x))/((x)!)`

`P(X = 1) = (e^(-2.40)*2.40^(1))/((1)!) = 0.2177`

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