The intersection of Easy Street and 69th Avenue averages 3 accidents every two days. Assuming the number of accidents follows a Poisson distribution:
What is the probability that there are exactly 8 accidents at that intersection in a week (7 days)?
Using Poisson's formula:
e^-9 * 9^8 / 8!
I got 9 since 3 accidents happens in two days so 3 * 3 equals a lambda of 9 in 6 days.
Got it wrong, what is the correct answer and solution?
Thinking of 10.5 since you add 1.5 from so that's the lambda for 7 days
An crucial first step in using the Poisson distribution is to use a rate $\lambda$ that exactly matches the question.
You are given that the accident rate for 2 days is $\lambda_2 = 3.$ So the rate for a week (7 days) is $\lambda_7 = 7(\lambda_2/2) = 10.5.$
Then the random variable $X$ that counts weekly accidents has $X \sim \mathsf{Pois}(\lambda_7 = 10.5),$ and you seek $P(X = 8) = e^{-10.5}10.5^8/8!.$ I will leave it to you do finish.
Note: You are on the right track, but you used $\lambda_6 = 9$ instead of $\lambda_7 = 10.5.$