I'm doing the following homework problem and am unsure of whether or not my answers are correct. This is my first time working with Poisson distribution and I want to make sure I am doing it correctly.
Suppose that the number of drivers who travel between a particular origin and destination during a designated time period has a Poisson distribution with mean $u = 20$. What is the probability that the number of drivers will
a. Be at most 10?
b. Exceed 20?
c. Be between 10 and 20, inclusive? Be strictly between 10 and 20?
d. Be within 2 standard deviations of the mean value?
I'm pretty much just trying to follow the formula that I was given for Poisson distribution and have the following answers:
a. $P(x\le 10) = \sum{0\to10}\frac {e^{20} \times 20^x}{x!} $
b. $P(x>20) = \frac {e^{20} \times 20^(20)}{20!} $
c. $P(10 \le x \le 20) = \sum_{10\to20}\frac {e^{20} \times 20^x}{x!} $
$P(10 < x <20) = \sum_{10\to20}\frac {e^{20} \times 20^x}{x!} $
d. not sure still
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