(11) Suppose that the IQ’s of East State University’s students are approximately normally distributed with mean 130 and standard deviation 8. Suppose that the IQ’s of West State University’s students are approximately normally distributed with mean 120 and standard deviation 10.

(a) If we select one student from each university, find the probability that the East State student’s IQ is at least 5 points higher than the West State student’s IQ.

(b) We select 3 West State students at random. Find the probability that their average IQ is at least 125.

(c ) We select 3 students from each school. Find the probability that the average IQ of the East State students is at least 5 points higher than the average for the West State students.