Question

Suppose the number of pages per book in a library has an unknown distribution with population mean 309 and population standard deviation 30. A sample of size n=50 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

Answer:

The standard deviation for the sample sum distribution is 212.13

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$, the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

For sums

Distribution is approximately normal with mean $n*\mu$ and standard deviation $\sqrt{n}*\sigma$

Using the Central Limit Theorem for Sums, what is the standard deviation for the sample sum distribution?

We have n = 50, $\sigma = 30$.

So

$\sqrt{50}*30 = 212.13$

The standard deviation for the sample sum distribution is 212.13