Suppose that the distribution of IQ's of North Catalina State University's students can be approximated by a normal model with m
ean 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?
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 = 0.7517
Step-by-step explanation:
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