The following graph shows the curve for a normally distributed variable. Superimposed are the curves for the sampling distributions of the sample mean for two different sample sizes.

A B

Normal curve for variable

a. Explain why all three curves are centered at the same place.

b. Which curve corresponds to the larger sample size? Explain your answer.

c. Why is the spread of each curve different?

d. Which of the two sampling-distribution curves corresponds to the sample size that will tend to produce less sampling error? Explain your answer.

e. Why are the two sampling-distribution curves normal curves?

Applying the Concepts and Skills