The number of road construction projects that take place at any one time in a certain city follows a Poisson distribution with a mean of 3. Find the probability that exactly four road construction projects are currently taking place in this city.

Using the Poisson distribution, it is found that there is a 0.1954 = 19.54% probability that exactly four road construction projects are currently taking place in this city.

We have only the mean for the discrete distribution, hence, the Poisson distribution is used.

The parameters are:

In this problem, the mean is of 3, hence .

The probability that exactly four road construction projects are currently taking place in this city is P(X = 4), hence:

0.1954 = 19.54% probability that exactly four road construction projects are currently taking place in this city.

You can learn more about the Poisson distribution at link

The probability that exactly four road construction projects are currently taking place in this city is 0.168.

Step-by-step explanation:

Let X denote the number of road construction projects that take place at any one time in a certain city.

It is provided that X follows a Poisson distribution with parameter λ = 3.

Then the probability mass function of X is:

Compute the probability that exactly four road construction projects are currently taking place in this city as follows:

Thus, the probability that exactly four road construction projects are currently taking place in this city is 0.168.