HOMEWORK 7-16

# HOMEWORK 7-16 - HOMEWORK 7 Due date Thursday March 10 at 4...

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HOMEWORK 7 Due date : Thursday March 10 at 4 pm 1. In any one-minute interval, the number of requests for a popular Web page is a Poisson random variable with expected value 300 requests. If the number of requests in a one minute interval is greater than n , where n is the capacity of the Web server, the server is overloaded. Use the central limit theorem to estimate the smallest value of n for which the probability of overload is less than 0.05. 2. Integrated circuits from a certain factory pass a certain quality test with probability 0.8. The outcomes of all tests are independent of each other. A total of 500 circuits are tested every day. What is the probability that more than 400 circuits will pass the quality test? 3. The lifetime of a cheap light bulb is an exponential random variable with mean 50 hours. Suppose that 25 light bulbs are tested and their lifetimes measured. What is the probability that the sum of the lifetimes is less than 1500 hours?
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