Question

The living spaces of all homes in a city have a mean of square feet and a standard deviation of square feet. Let be the mean living space for a random sample of homes selected from this city. Find the mean of the sampling distribution of . Enter an exact answer. mean of square feet Find the standard deviation of the sampling distribution of . Round your answer to one decimal place. standard deviation of square feet

Answer 1

Answer:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

The mean for this case is given by:

$\mu_{\bar X} = 2300.0$

And the deviation would be:

$\sigma_{\bar X}= \frac{500}{\sqrt{25}}= 100.0$

Step-by-step explanation:

Using the following problem info since is incomplete the data: "The living spaces of all homes in a city have a mean of 2300 square feet and a standard deviation of 500 square feet. Let x be the mean living space for a random sample of 25 homes selected from this city.  Find the mean and standard deviation of the sampling distribution of x."

We know the following info given:

$\mu = 2300$ represent the mean for tehe living spaces of all homes in a city

$\sigma = 500$ represent the population deviation for the data

We select a sample size of n=25 so then this size is large enough in order to use the central limit theorem and we can use for the distribution of the sampel mean:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

The mean for this case is given by:

$\mu_{\bar X} = 2300.0$

And the deviation would be:

$\sigma_{\bar X}= \frac{500}{\sqrt{25}}= 100.0$