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

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

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

`P(X = 0) = (e^(-4)*(4)^(0))/((0)!) = 0.0183`

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