Questions:
 #1:-

	Among all applicants to a certain university, the Math
	SAT scores averaged 535 with a SD of 100. If the normality
    	assumption is reasonable, do the following: 

        a) An applicant scored 750 on the Math SAT. Determine the
           percentile rank of this score.

        b) Determine the score corresponding to the 80th percentile.


 #2:-

        For freshmen at some other university, the average GPA is 3.0 
	with a SD of 0.5. If normality is reasonable, determine the
        score correponding to the 30th percentile.





Solutions:-
 #1(a):-

	You need to determine the proportion of scores that are less
	than 750:
                 z = (750 - 535)/100
                   = 2.15
        Since 96.84% of scores are between -2.15 and 2.15 then the
        percentile rank is 96.84+(100-96.84)/2=98.42.  
 
 #1(b):-

	The z score in this case is 0.85. Remember that 20% of scores
        will be to the right of z since we are interested in the 80th
	percentile. If this is so then 20% are to the left of -z and
	so the percentage needed in the table is 60.
        The desired x value is: 
			x=0.85(100)+535=620
	The score correponding to the 80th percentile is therefore 620.

 #2:-

	The z score in this case is -0.5. In this case 30% of scores
        will be to the left of -z since we are interested in the 30th
	percentile. If this is so then 30% are to the right of z and
	so the percentage needed in the table is 40.
        The desired x value is: 
			x=-0.5(0.5)+3.0=2.75
	The GPA correponding to the 30th percentile is therefore 2.75.