Question 194883
An insurance company has an average of 9 claims per week.  What is the probability that during the next week exactly 7 will be filed.
<pre><font size = 4 color = "indigo"><b>
If X is the number of successes in an interval
of fixed length and X follows a Poisson process 
with mean {{{mu}}}, then the probability that 
X = x is
         
{{{P(X=x) = ((mu^x)/x!)e^(-mu)}}}
         
In your problem, {{{mu=9}}}, {{{x=7}}}, so

{{{P(X=7) = ((9^7)/7!)e^(-9)=.1171161245}}} 

Edwin</pre>