Question

Use the Central Limit Theorem to find the mean and standard error of the mean of the indicated sampling distribution. The monthly rents for studio apartments in a certain city have a mean of $ 1 comma 060 and a standard deviation of $ 190. Random samples of size 30 are drawn from the population and the mean of each sample is determined. Round the answers to the nearest hundredth.

Answer 1

Answer:

Mean $1060

Standard error $34.69

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, which is also called standard error, $s = \frac{\sigma}{\sqrt{n}}$.

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

Population:

Mean $1,060 and standard deviation $190.

Sampling distriution of samples of size 30:

Mean $1060

Standard deviation $s = \frac{190}{\sqrt{30}} = 34.69$