A random sample of size n1 = 16 is selected from a normal population with a mean of 75 and a standard deviation of 8. A second random sample of size n2 = 9 is taken from another normal population with a mean of 70 and a standard deviation of 12. Let X1 and X2 be the two sample means. Find the following:

a) The probability that X1 − X2 exceeds 4

b) The probability that 3.5 ≤ X1_(bar) − X2_(bar) ≤ 5.5.