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 is 1.15.

Step-by-step explanation:

The standard deviation for the sample sum distribution can be calculated using the Central Limit Theorem for Sums. According to the theorem, the standard deviation is equal to the population standard deviation divided by the square root of the sample size. In this case, the population standard deviation is 10, and the sample size is 75. Therefore, the standard deviation for the sample sum distribution is 10 / sqrt(75) = 1.15. Rounded to two decimal places, the standard deviation is 1.15.