Question

The mean is 47.1 and the standard deviation is 9.5 for a population. Using the Central Limit Theorem, what is the standard deviation of the distribution of sample means for samples of size 60

Answer 1

Answer:

The standard deviation of the distribution of sample means for samples of size 60 is of 1.2264.

Step-by-step explanation:

Central Limit Theorem

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

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Standard deviation is 9.5 for a population.

This means that $\sigma = 9.5$

Sample of 60:

This means that $n = 60$

What is the standard deviation of the distribution of sample means for samples of size 60?

$s = \frac{\sigma}{\sqrt{n}} = \frac{9.5}{\sqrt{60}} = 1.2264$

The standard deviation of the distribution of sample means for samples of size 60 is of 1.2264.