Question

A random variable is not normally distributed, but it is mound shaped. It has a mean of 11 and a standard deviation of 4.

Answer 1

Using the Central Limit Theorem, nothing can be stated about the shape of the sampling distribution for the sample mean, as the sample size is less than 30.

What does the Central Limit Theorem state?

It states that, for a normally distributed 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 sampling distribution is also approximately normal, as long as n is at least 30.

In this problem, we have a skewed variable and n < 30, hence nothing can be stated about the shape of the sampling distribution for the sample mean.

More can be learned about the Central Limit Theorem at brainly.com/question/16695444

#SPJ1