STATS 1430 Review

Yes, because X has a normal distribution already.

If X has a normal distribution, could you find a probability for (x-bar) if n Xwas only 10?

True

If the values in the population are skewed, the sampling distribution of (x-bar) can be approximated by the normal distribution if the sample contains at least 30 observations.

Approximately normal for large enough samples by the Central Limit Theorem

Let (x-bar) be the sample mean from X's distribution. Suppose X does not X have a normal distribution. The distribution (shape) of (x-bar) is:

(x-bar) has an exact normal distribution for any value of n.

Suppose X has a normal distribution and (x-bar) represents the average of a sample of size n. Which of the following is true?

For n large, it says the distribution of the sample mean is approximately normal, regardless of the shape of the population.

The Central Limit Theorem is important in statistics because:

Is approximately normal if n ≥ 30

The Central Limit Theorem states that, if a random sample of size n is drawn from a population, then the sampling distribution of the sample mean (x-bar)