Question

Suppose the 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?

a. The mean of the sampling distribution of X is 800.


b.The standard deviation of the sampling distribution of X is 16.


c.The value of every sample mean is 800The sampling distribution of X will be approximately normal regardless of sample size.

Answer 1

a. The mean of the sampling distribution of X is 800.

Explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean
`\mu` and standard deviation
`\sigma`, a large sample size of the sampling distribution can be approximated to a normal distribution with mean
`\mu` and standard deviation
`s = (\sigma)/(√(n))`.

So, the correct answer is

a. The mean of the sampling distribution of X is 800.