A sample of size nn is randomly selected from a non-normal population with mean and standard deviation .

a. Describe the mean and standard deviation of the sampling distribution of XX for all samples of size nn selected from this population.

The Central Limit Theorem (CLT) states that if

(click to select)n 30n 30n 5n 5

, then the sampling distribution of sample means is reasonably approximated by a

(click to select)F distribution Normal distribution Poisson distribution Uniform distribution

. The mean of the sampling distribution of xx , denoted xx , is

(click to select) equal not equal

to the underlying population mean . The standard deviation of the sampling distribution of xx , denoted xx , is called the

(click to select) standard deviation normal deviation standard error normal error

of the mean and is equal to nn .

b. Describe the shape of the sampling distribution in if n=150n=150

For n=150n=150 , the distribution of sample means very well approximates the normal distributions, and is bell-shaped.

For n=150n=150 , since the initial distribution is non-normal, the distribution of sample means does not approximates the normal distributions, and depends on the initial distribution.