Question

The pages per book in a LiBrary have an unknown distribution with mean 316 and standard deviation 20 pages. A sample, with size n=40, is randomly drawn from the population and the values are added together. Using the central limit theorem for sums, what is the mean for the sample sum distribution?

Answer 1

The mean for the sample sum distribution using the Central Limit Theorem for Sums is 12640 pages, given the population mean is 316 pages and the sample size is 40.

Step-by-step explanation:

The student is asking about the application of the Central Limit Theorem for Sums to calculate the mean of the sample sum distribution for a randomly drawn sample from a library with books that have an average of 316 pages and a standard deviation of 20 pages. Given that the sample size (n) is 40, according to the Central Limit Theorem, the mean for the sample sum distribution (μsum) is computed by multiplying the population mean (μx) by the sample size (n). Hence, μsum = n * μx = 40 * 316 = 12640 pages.