Estimating Web Server Capacity using Central Limit Theorem

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In anyone minute interval, the number of requests for a popular web page is a poisson random variable with expected value 300 requests.

a) a web server has a capacity of C requests per minute. if the number of requests in a one minute interval is greater than C, the server is overloaded. Use the central limit theorem to estimate the smallest value of C for which the probability of overload is less than 0.05
 
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Another statement of a problem with no attempt at all to solve it! We are not going to do your homework for you. Since you apparently at least know this problem is connected with the "central limit theorem", what is the central limit theorem and how can you apply it to this problem?
 
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There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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