6. There are two classes, one of size 36 and the other of size 64. The exam scores of students in these classes are i.i.d. random variables with mean 77 pts and standard deviation 15 pts. (a) What normal distribution approximates the average test score in the class of size 36? (b) What normal distribution approximates the average test score in the class of size 64? (c) What is the approximate probability that the average test score in the class of size 36 is higher than that in the class of size 64 by 5 pts? (No need to use the correction for continuity nor computing the final numerical value.) (d) Suppose the average scores in the two classes are 76 and 83. Which class do you think was more likely to have averaged 83? (It suffices to explain the answer intuitively.)