The average score for an MechE student on a statistics test in their senior year is believed to be 89.0 in the population, with a standard deviation of 5.0. A random sample of scores for 121 MechE seniors is taken from national records. The average score on this test for CivE seniors is believed to be 85.0 with a standard deviation of 10.0 in the population. A random sample of scores for 121 CivE seniors is also taken. a) What is the probability the sample average score for CivE seniors is less than the sample average score for MechE seniors by more than 10.0?

b) What knowledge about the sample averages must you use in determining the answer to Part a, and what is your justification in using this knowledge?