Estimating Web Server Capacity using Central Limit Theorem

In summary, the central limit theorem can be applied to estimate the smallest value of C for which the probability of overload is less than 0.05 for a web server with a capacity of C requests per minute, given that the number of requests for a popular web page in a one minute interval follows a Poisson distribution with an expected value of 300 requests.
  • #1
hxluo
14
0
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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  • #2
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?
 
  • #3
ddfasdfsdfs
 

What is the Central Limit Theorem?

The Central Limit Theorem (CLT) is a fundamental concept in statistics that states that when independent random variables are added, their sum tends to follow a normal distribution, even if the individual variables themselves do not.

Why is the Central Limit Theorem important?

The CLT is important because it allows us to make certain assumptions about a population's distribution, even if we do not have complete information about it. This allows for the use of powerful statistical tools and methods for making inferences and drawing conclusions.

What are the assumptions of the Central Limit Theorem?

The main assumptions of the CLT are that the sample size is sufficiently large (typically n ≥ 30), the variables are independent, and the sample is taken from a population with finite variance.

What is the relationship between the Central Limit Theorem and the Law of Large Numbers?

The Law of Large Numbers and the Central Limit Theorem are related, but they are not the same. The Law of Large Numbers states that as the sample size increases, the sample mean gets closer to the population mean. The Central Limit Theorem, on the other hand, deals with the distribution of the sample mean, and states that it tends towards a normal distribution as the sample size increases.

How is the Central Limit Theorem used in practice?

The CLT is used in many areas of statistics, such as hypothesis testing, confidence intervals, and regression analysis. It allows us to make assumptions about a population's distribution and use statistical tools to make inferences and draw conclusions based on sample data.

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