Question

Determine mu subscript x overbarμx and sigma subscript x overbarσx from the given parameters of the population and the sample size. round the answer to the nearest thousandth where appropriate. muμequals=3232​, sigmaσequals=77​, nequals=23

Answer 1

`\bar X \sim N(\mu, (\sigma)/(√(n)))`

And replacing we got:

`\mu_(\bar X)= 32`

`\sigma_(\bar X) = (77)/(√(23)) =10.06`

Explanation:

Previous concepts

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Let X the random variable who represents the variable of interest, with the following properties:

`\mu =32,\sigma =77`

We select a sample of n=23 nails.

From the central limit theorem we can approximate that the distribution for the sample mean
`\bar X` is given by:

`\bar X \sim N(\mu, (\sigma)/(√(n)))`

And replacing we got:

`\mu_(\bar X)= 77`

`\sigma_(\bar X) = (77)/(√(23)) =10.06`