Question

Suppose the number of pages per book in a library has an unknown distribution with population mean 238 and population standard deviation 10 . A sample of size n=75 is randomly taken from the population, and the sum of the values is taken. Using the Central Limit Theorem for Sums, what is the standard deviation for the sample sum distribution? Round your answer to two decimal places.

Answer 1

The standard deviation for the sample sum distribution, given a population mean of 238 and a population standard deviation of 10 with a sample size of 75, is approximately 86.60 when rounded to two decimal places.

Step-by-step explanation:

The student is focused on applying the Central Limit Theorem for Sums to calculate the standard deviation of the sample sum distribution in a statistics problem. We are given a population mean (μ) of 238 and a population standard deviation (σ) of 10. A sample of size n = 75 is considered for the sum of the values.

To find the standard deviation for the sample sum, we multiply the population standard deviation by the square root of the sample size:

σsum = σ * √n
σsum = 10 * √75
σsum = 10 * 8.66
σsum = 86.6 (rounded to two decimal places)

Therefore, the standard deviation for the sample sum distribution is approximately 86.60.