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:
![P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20%5Cfrac%7Be%5E%7B-%5Cmu%7D%2A%5Cmu%5E%7Bx%7D%7D%7B%28x%29%21%7D)
In which
x is the number of sucesses
e = 2.71828 is the Euler number
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 ![\mu = 5*0.25 = 1.25](https://tex.z-dn.net/?f=%5Cmu%20%3D%205%2A0.25%20%3D%201.25)
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
![P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20%5Cfrac%7Be%5E%7B-%5Cmu%7D%2A%5Cmu%5E%7Bx%7D%7D%7B%28x%29%21%7D)
![P(X = 0) = \frac{e^{-1.25}*(1.25)^{0}}{(0)!} = 02865](https://tex.z-dn.net/?f=P%28X%20%3D%200%29%20%3D%20%5Cfrac%7Be%5E%7B-1.25%7D%2A%281.25%29%5E%7B0%7D%7D%7B%280%29%21%7D%20%3D%2002865)