Percentile Problem:

	Question:-

	HP releases a new model with a MIPS rating of 310. What is the 
	percentile rank of this model. Assume that the mean MIPS rating
	of all workstations is 200 with a SD of 50.

	Solution:-

	We need to find the proportion of workstations with a MIPS rating
	of 310 or less.
			z=(310-200)/50=2.2 
	For a z score of 2.2 the percentage from the standard normal table
	is 97.22. The percentile rank is therefore 97.22+(100-97.22)/2. 
	The percentile rank is therefore 98.61.


	Question:-

	What if HP had claimed that the MIPS rating for this model was in the
	99th percentile. How would you validate this claim.

	Solution:-

	First find the z score for which 99% of observations are less than or
	equal to it. That is, find from the standard normal table the z value
	for an area of 98%. The z score is 2.35 (approx).
			2.35=(unknown-200)/50
    	Then solve for the unknown value that defines the 99th percentile:
		     unknown=50(2.35)+200
			    =317.5
	Since 317.5 is greater than 310 HP's claim is invalid. 
	


Regression Problem:

	Question:-

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

	Solution:-

	You should first note that we are interested in workstations with a 
	particular MIPS rating of 300. Note also that benchmark must be the
	y axis.

	STEP 1: Determine the average benchmark score for workstations with a
		MIPS rating of 300. 
			rise/100=-0.8(300/50)
			    rise=-480
		Hence 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 also score less than 1500 on the standard 
		benchmark.