The average score on the Writing part of the SAT exam for males is 486 with a standard deviation of 112, while the average score for females is 498 with a standard deviation of 111.
(a) If random samples are taken with 100 males and 100 females, find the mean and standard deviation of the distribution of differences in sample means, x̅_m − x̅_f , where x̅_m represents the sample mean for the males and x̅_f represents the sample mean for the females.
(b) Repeat part (a) if the random samples contain 500 males and 500 females.
(c) What effect do the different sample sizes have on center and spread of the distribution?

involve scores from the high school graduating class of 2010 on theSAT(Scholastic Aptitude Test).