Question

What is the probability of observing exactly three accidents on this stretch of road next month?

Answer 1

Using the Poisson distribution, the probability of observing exactly three accidents on this stretch of road next month is given by:

b) 0.052.

What is the Poisson distribution?

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

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

The parameters are:

• x is the number of successes

• e = 2.71828 is the Euler number

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

Researching this problem on the internet, the mean is given by:

$\mu = 7$.

The probability of observing exactly three accidents on this stretch of road next month is P(X = 3), hence:

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

$P(X = 3) = \frac{e^{-7}7^{3}}{(3)!} = 0.052$

Hence option B is correct.

More can be learned about the Poisson distribution at brainly.com/question/13971530

#SPJ4