Suppose that the distribution of IQs of North Catalina State

Suppose that the distribution of IQ\'s of North Catalina State University\'s students can be approximated by a normal model with mean 130 and standard deviation 8 points. Also suppose that the distribution of IQ\'s of Chapel Mountain University\'s students can be approximated by a normal model with mean 120 and standard deviation 10 points.

Question 1. You select 3 students at random from each school. What is the probability that the mean IQ of the 3 North Catalina students is at least 5 points higher than the mean IQ of the 3 Chapel Mountain students?

Solution

hre let A =X-Y where X and Y are IQ of 3 North Catalina student and mean IQ of the 3 Chapel Mountain students

hence expected value of A =130-120 =10

std error of mean difference =(8²/3+10²/3)^1/2 =7.3937

hence probability that the mean IQ of the 3 North Catalina students is at least 5 points higher than the mean IQ of the 3 Chapel Mountain students =P(A>5)=P(Z>(5-10)/7.3937)=P(Z>-0.68)=0.7517