The Critical Reading portion of the Scholastic Aptitude Test (SAT) was taken by 1,547,990 college bound students in the class of 2010. Scores on that portion of the test range from 200 to 800 and the average score for the class of 2010 is 501 with a standard deviation of 112. Scores are approximately normally distributed.

(a) For each sample size below, give the mean and standard deviation of the distribution of the sample means:

i. n = 1

ii. n = 10

iii. n = 100

iv. n = 1000

(b) Considering your answers from part (a), discuss the effect of the sample size on the center and variability of the distribution of sample means.