Section 8.1 Homework 

3.  A simple random sample of size n=40 is obtained from a population with ì=64 and ó=9. Does the population need to be normally distributed for the sampling distribution of x to be approximately normally​ distributed? Why? What is the sampling distribution of x​?Does the population need to be normally distributed for the sampling distribution of x to be approximately normally​ distributed? Why?

1. No because the Central Limit Theorem states that regardless of the shape of the underlying​ population, the sampling distribution of x becomes approximately normal as the sample​ size, n, increases.
2. Yes because the Central Limit Theorem states that only for underlying populations that are normal is the shape of the sampling distribution of x ​normal, regardless of the sample​ size, n.
3. No because the Central Limit Theorem states that only if the shape of the underlying population is normal or uniform does the sampling distribution of x become approximately normal as the sample​ size, n, increases.
4. Yes because the Central Limit Theorem states that the sampling variability of nonnormal populations will increase as the sample size increases.

What is the sampling distribution of x​?

Select the correct choice below and fill in the answer boxes within your choice.

The sampling distribution of x is skewed left with μx=nothing and σx=nothing.

The sampling distribution of x follows​ Student’s t-distribution with μx=nothing and σx=nothing.

The sampling distribution of x is normal or approximately normal with μx=6464 and σx=1.4231.423.

The sampling distribution of x is uniform with μx=nothing and σx=nothing.