Question

g A variable of a population has a mean mu equals 100 and a standard deviation sigma equals 21. a. The sampling distribution of the sample mean for samples of size 49 is approximately normally distributed with mean and standard deviation of

Answer 1

Answer:

The sampling distribution of the sample mean for samples of size 49 is approximately normally distributed with mean of 100 and standard deviation of 3.

Step-by-step explanation:

The Central Limit Theorem estabilishes 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.

Population

Mean 100, standard deviation 21.

The sampling distribution of the sample mean for samples of size 49

By the Central Limit Theorem

Mean 100

Standard deviation

$s = \frac{21}{\sqrt{49}} = 3$

The sampling distribution of the sample mean for samples of size 49 is approximately normally distributed with mean of 100 and standard deviation of 3.