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

`\bar X= \mu = 25`

`\sigma_(\bar X)= (7)/(√(15))= 1.807`

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, (\sigma)/(√(n)))`

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

`\bar X= \mu = 25`

`\sigma_(\bar X)= (7)/(√(15))= 1.807`