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:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] 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 [tex]\mu = 4[/tex]
What is the probability there are no car accidents on that stretch on Monday?
This is P(X = 0).
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-4}*(4)^{0}}{(0)!} = 0.0183[/tex]
1.83% probability there are no car accidents on that stretch on Monday
