document.write( "Question 866796: Please help me solve this problem.\r
\n" ); document.write( "\n" ); document.write( "The combined math and verbal scores for students taking a national standardized examination for college admission, is normally distributed with a mean of 530 and a standard deviation of 180. If a college requires a student to be in the top 30% of students taking this test, what is the minimum score that such a student can obtain and still qualify for admission at the college?\r
\n" ); document.write( "\n" ); document.write( "thank you! \n" ); document.write( "
Algebra.Com's Answer #522513 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
mean is 530
\n" ); document.write( "standard deviation is 180
\n" ); document.write( "you want to find the z-score where 30% of the students will have z-scores higher than that, which means that 70% of the students will have z-scores lower than that.
\n" ); document.write( "you need to look in the z-score table to find an area to the left of the z-score that is equal to .70 or very close to it.
\n" ); document.write( "the z-score table used for this problem can be found at the following link:
\n" ); document.write( "follow this link to z-score table used in this problem.
\n" ); document.write( "looking at this table, you will see that there are 2 areas that flank .7
\n" ); document.write( "those areas are .6985 and .7019
\n" ); document.write( "looking at the z-scores for those area, you will see that the z-scores are:
\n" ); document.write( "z = .53 for an area of .7019 to the left of that z-score.
\n" ); document.write( "z = .52 for an area of .6985 to the left of that z-score.
\n" ); document.write( "now you want to translate those z-score into raw scores.
\n" ); document.write( "the formula for z-score is:
\n" ); document.write( "z-score = (x - m) / sd
\n" ); document.write( "x = raw score
\n" ); document.write( "m = mean
\n" ); document.write( "sd = standard deviation.
\n" ); document.write( "since m = 530 and sd = 180, the formula becomes:
\n" ); document.write( "z = (x - 530) / 180
\n" ); document.write( "when z is equal to .53, this formula becomes:
\n" ); document.write( ".53 = (x-530) / 180
\n" ); document.write( "solve for x to get x = 625.4
\n" ); document.write( "when x is equal to .52,this formula becomes:
\n" ); document.write( ".52 = (x-530) / 180
\n" ); document.write( "solve for x to get x = 623.60
\n" ); document.write( "the minimum score to get into college is going to be between 623.60 and 625.4
\n" ); document.write( "to be on the same side, figure 625.4
\n" ); document.write( "to be more exact, you can interpolate, or you would use a calculator that gives you the answer to more decimal places.
\n" ); document.write( "the TI-84 calculator will tell you that the more exact z-score for an area of .7 to the left of that z-score will be:
\n" ); document.write( "z = .524400510
\n" ); document.write( "that corresponds to a raw score of:
\n" ); document.write( ".524400510 = (x - 530) / 180
\n" ); document.write( "solve for x to get:
\n" ); document.write( "x = 624.3920918
\n" ); document.write( "it's a matter of how close you need to get the answer.
\n" ); document.write( "if rounding the z-score to 2 decimal places is as detailed as you need to get, then the answer is 625.4 from a z-score of .53.
\n" ); document.write( "that ensures your score is greater than 70% of the population scores.\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );