Question

Heights for women are bell-shaped with a mean of 65 inches and standard deviation of 2.5 inches. If a random sample of 16 women is taken, what is the mean and standard deviation of the sampling distribution of ? μ= 65 inches; σ= 0.625 inch μ= 65 inches; σ= 2.5 inches μ= 65 inches; σ= 0.156 inch μ= it depends on the value of the sample mean ; σ= it depends on the value of the sample standard deviation

Answer 1

Answer:

μ= 65 inches; σ= 0.625 inch

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed(bell-shaped) random variable X, with mean $\mu$ and standard deviation $\sigma$, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\mu = 65, \sigma = 2.5$

By the central limit theorem, the sample of 16 will have:

$\mu = 65, \sigma = \frac{2.5}{\sqrt{16}} = 0.625$

So the correct answer is:

μ= 65 inches; σ= 0.625 inch