Answer:
The answer is 0.2865
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.
In this problem, we have that:
The mean number of accidents on any given day in Coralville is 5. Of those, 25% are with an uninsured drive.
So [tex]\mu = 5*0.25 = 1.25[/tex]
Calculate the probability that on a given day in Coralville there are no trafficaccidents that involve an uninsured driver.
This is P(X = 0). So
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-1.25}*(1.25)^{0}}{(0)!} = 02865[/tex]
