In any one-minute interval, the number of requests for a popular Web page is a Poisson random variable with expected value 180 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 0.055. Note that your answer must be an integer. Also, since this is a discrete random variable, don't forget to use "continuity correction".
(b) Now assume that the server's capacity in any one-second interval is ⌊C/60⌋, where ⌊x⌋ is the largest integer ≤x. (This is called the floor function.) For the value of C derived in part (a), what is the probability of overload in a one-second interval? This time, don't approximate via the CLT, but compute the probability exactly.