Question

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 6. Find the probability that less than 3 road construction projects are currently taking place in this city.a) 0.050409b) 0.089235c) 0.301168d) 0.014936

Answer 1

The probability that less than 3 road construction projects are currently taking place in this city is 0.06197

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.

Poisson distribution with a mean of 6.

This means that
`\mu = 6`

Find the probability that less than 3 road construction projects are currently taking place in this city.

This is:

`P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)`

So

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

`P(X = 0) = (e^(-6)*6^(0))/((0)!) = 0.00248`

`P(X = 1) = (e^(-6)*6^(1))/((1)!) = 0.01487`

`P(X = 2) = (e^(-6)*6^(2))/((2)!) = 0.04462`

`P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.00248 + 0.01487 + 0.04462 = 0.06197`

The probability that less than 3 road construction projects are currently taking place in this city is 0.06197