In order to ensure efficient usage of a server, it is necessary to estimate the

Question

In order to ensure efficient usage of a server, it is necessary to estimate the mean number of concurrent users. According to records, the sample mean and sample standard deviation of number of concurrent users at 50 randomly selected times is 37.7 and 9.2, respectively. a. Construct a 90% confidence interval for the mean number of concurrent users. b. Historical records indicate there has never been less than 20 or more than 60 concurrent users on the server. How many users should be sampled if you want to construct a confidence interval for the mean number of concurrent users with a margin of error of ± 5 users? Please, no handwritten answers.

Explanation / Answer

here std error =std deviation/(n)1/2 where n=50

=1.301

for 90% CI, z=1.6448

hence CI=mean +/- z*std error =35.5599 ; 39.8401

b) here margin of errorr E=5

sample size=(Z*std deviation/E)2 ~10

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