Question

The number of accidents on a certain section of I-40 averages 4 accidents per weekday independent across weekdays. Assuming the number of accidents on a day follows a Poisson distribution.
What is the probability there are no car accidents on that stretch on Monday?

Answer 1

Answer:

1.83% probability there are no car accidents on that stretch on Monday

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 time interval.

The number of accidents on a certain section of I-40 averages 4 accidents per weekday independent across weekdays.

This means that $\mu = 4$

What is the probability there are no car accidents on that stretch on Monday?

This is P(X = 0).

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

$P(X = 0) = \frac{e^{-4}*(4)^{0}}{(0)!} = 0.0183$

1.83% probability there are no car accidents on that stretch on Monday