A biology professor is teaching sections A and B of BIOL1000. the professor knows from the past that student exam marks of section A follow a normal distribution with an average of 65, and a standard deviation of 10 while the student's exam marks of section B follow a normal distribution with an average of 70 and a standard deviation of 20.

a) find the probability that the average exam marks by a random sample of 100 students in section B is less than 67

b) what is the probability that the average marls for 81 randomly selected students from section A is one mark higher than the average exam marks of 100 randomly selected students from section B? c) The professor declares that no more than one-quarter of section B's students will get average marks. what is the probability that in a random sample of the 80 section B students, more than 2Y9, 8 will get average marks?