Question:-

	A sample of workstations is collected and the MIPS rating and score
	on a standard benchmark recorded for each machine. A data analyst is
	interested in predicting benchmark score from MIPS rating and is
	also interested in making inferences for workstations with a
	particular MIPS rating.

	Given an average MIPS rating of 200 with a SD of 50 and an average
	benchmark score of 1800 with a SD of 300 and given a correlation of
	-0.8 between MIPS rating and benchmark score.

	Find the proportion of workstations with a MIPS rating of 300 that had
	a score of less than 1500 on the benchmark. Make necessary assumptions.

Solution:-

	You should first note that we are interested in predicting benchmark
        score. Hence, benchmark score must be on the y axis and MIPS rating
        on the x-axis. Note also that we are interested in workstations with  
	a particular MIPS rating (i.e. 300).

	STEP 1: Determine the average benchmark score for workstations with a
		MIPS rating of 300. 

                There are two ways of doing this:

                1. Derive the regression equation and plug in 300:
                        b=-0.8(300/50)=-4.8
                        a=1800-(-4.8(200))=1800+960=2760
                   Hence:
                        y=2760-4.8(300)=2760-1440=1320
                   Benchmark score is therefore 1320 for a MIPS rating
                   of 300.

		2. You may also arrive at this answer by using the
                   following method:

                   Remember that slope = (rise/run). Since we know that
                   (xbar, ybar) is on the regression line we can compute
                   the rise since the run is 100:
                	rise/100=-0.8(300/50)
			    rise=-480
		   Hence benchmark score is 1800-480=1320.

	STEP 2: Determine the SD for these workstations.

			SD(y|x)=sqrt(1-(-0.8)**2)SD(y)
			SD(y|x)=sqrt(1-0.64)300
			       =180

	STEP 3: Assume NORMALITY and find the proportion less than 1500. 
			z=(1500-1320)/180=1
		Hence 84.14% or approximately 84% of workstations with a MIPS
		rating of 300 have a  score less than 1500 on the standard 
		benchmark.