Question

Suppose that distribution of the daily calcium intake of Americans is left skewed with a mean of 800 mg and a standard deviation of 16 mg. what can we say about the sampling distribution of distribution X with bar on top

Answer 1

Answer:

Explained below.

Step-by-step explanation:

According to the Central Limit Theorem if an unknown population is selected with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from this population with replacement, then the distribution of the sample means will be approximately normal.

Then, the mean of the sampling distribution of sample means is given by,

$\mu_{\bar x}=\mu$

And the standard deviation of the sampling distribution of sample means is given by,

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}$

So, if the sample of daily calcium intake of Americans collected is more than 30, then the sampling distribution of $\bar X$ will be approximately normal.