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

Mean $1060

Mean $1060Standard error $34.69

Answer 2

Mean $1060

Standard error $34.69

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 = (\sigma)/(√(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 = (190)/(√(30)) = 34.69`