Question

Determine mu Subscript x overbar and sigma Subscript x overbar from the given parameters of the population and the sample size. Round the answer to the nearest thousandth where appropriate. muequals25​, sigmaequals7​, nequals15

Answer 1

Answer:

$\bar X= \mu = 25$

$\sigma_{\bar X}= \frac{7}{\sqrt{15}}= 1.807$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the variable of interest of a population, and for this case we know the following conditions

Where $\mu=25$ and $\sigma=7$

And for this case we select a sample size of n= 15. and we want to know the distribution for the sample mean $\bar X$. We can assume that the distribution for $\bar X$ is approximately normal and given by:

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

Asuming that the distribution for X is also approximately normal. So then the parameters are:

$\bar X= \mu = 25$

$\sigma_{\bar X}= \frac{7}{\sqrt{15}}= 1.807$