Question

A random sample is selected from a population with mean = 100 and standard deviation = 10. Determine the mean and standard deviation of the x sampling distribution for each of the following sample sizes. (Round the answers to three decimal places.)
If N=41
If N=130

Answer 1

The mean and standard deviation of the x sampling distribution for each of the following sample sizes will be $N(100,10/\sqrt{41} ), N(100,10/\sqrt{130} )$.

What is the distribution of the sample mean for large samples?

Suppose X has a distribution with mean $\mu$ and standard deviation $\sigma,$then,

the distribution of the mean of samples of size n, drawn from the values of X, is normally distributed with a mean equal to the mean of X, and a standard deviation equal to $\sigma/\sqrt{n}$

Symbolically, we write it as:

$X \sim N(\mu, \sigma) \implies \overline{X} \sim N(\mu,\sigma/\sqrt{n} )$

A random sample is selected from a population with a mean = of 100 and a standard deviation = of 10.

The mean and standard deviation of the x sampling distribution for each of the following sample sizes.

If N=41

$X \sim N(100, 10) \implies \overline{X} \sim N(100,10/\sqrt{41} )$

If N=130

$X \sim N(100, 10) \implies \overline{X} \sim N(100,10/\sqrt{130} )$

Learn more about standard normal distribution here:

brainly.com/question/10984889

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