An experiment on the teaching of reading compares two methods, A and B. The outcome variable is the Degree of Reading Power (DRP) score. The experimenter uses Method A in a class of 26 students and Method B in a comparable class of 24 students. The classes are assigned to the teaching methods at random. Suppose that in the population of all children of this age, the DRP score ~N(34, 12) if Method A is used and is ~N(37, 11) if Method B is used.

a) What is the distribution of the mean DRP score for the 26 students in group A? Assume that this group can be regarded as a SRS from the population of all children of this age.

b) What is the distribution of the mean DRP score for the 24 students in the B group? Assume that this group can be regarded as a SRS from the population of all children of this age.

c) Use the results of (a) and (b), keeping in mind that A and B are independent, to find the distribution of the difference between the mean scores for the two groups, i.e., ABXX.

d) What is the probability that the mean score for the B group will be at least 4 points higher than the mean score for the A group?