100 POINTS Suppose that IQs of East State University’s students can be described by a Normal model with mean 140 and standard deviation 6 points. Also suppose that IQs of students from West State University can be described by a Normal model with mean 130 and standard deviation 9.

a) We select a student at random from East State. Find the probability that this student’s IQ is at least 130 points.
b) We select a student at random from each school. Find the probability that the East State student’s IQ is at least 5 points higher than the West State student’s IQ.
c) We select 3 West State students at random. Find the probability that this group’s average IQ is at least 130 points.
d) We also select 3 East State students at random. What’s the probability that their average IQ is at least 5 points higher than the average for the 3 West Staters?