Question #1:-

	HP releases a new model with a MIPS rating of 310. Determine the  
	percentile rank for 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 
	which is 98.61.


Question #2:-

	What if an independent testing organization wanted to know the
	MIPS rating corresponding to the 90th percentile. Assume the mean
        and SD above.

Solution:-

	We need to find the MIPS rating (x) so that 90% of workstations 
	have ratings less than x. The z score in this case is 1.3 since
        from the standard normal table 80% of observations are between
        -1.3 and 1.3. The desired x value is: 
			x=1.3(50)+200=265
	The MIPS rating correponding to the 90th percentile is therefore
        265.


Question #3:-

	What if HP had claimed that the MIPS rating for the model in 
	question #1 is 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.