Suppose that IQs of East State University s students can be described by a Normal model with mean 130 and standard deviation 8 points. Also suppose that IQs of students from West State University can be described by a Normal model with mean 120 and standard deviation 10.
a) We select a student at random from East State. Find the probability that this student s IQ is at least 125 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 125 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?