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 ofCrequests per minute. If the number of requests in a one-minute interval is greater thanC,the server is overloaded. Use the central limit theorem to estimate the smallest value ofC for which the probability of overload is less than 0.05.

b) Now assume that the server's capacity in any one-second interval isC/60.

For the value ofC derived in part (a), what is the probability of overload in a one-second interval?