Question 866796: Please help me solve this problem.
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?
thank you!
Found 2 solutions by ewatrrr, Theo:
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!
Hi
mean of 530 and a standard deviation of 180
invNorm(.70) = .5244
.5244 = (X-530)/180
180(.5244) + 530 = 624.392, 625 min for admission
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! mean is 530
standard deviation is 180
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.
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.
the z-score table used for this problem can be found at the following link:
follow this link to z-score table used in this problem.
looking at this table, you will see that there are 2 areas that flank .7
those areas are .6985 and .7019
looking at the z-scores for those area, you will see that the z-scores are:
z = .53 for an area of .7019 to the left of that z-score.
z = .52 for an area of .6985 to the left of that z-score.
now you want to translate those z-score into raw scores.
the formula for z-score is:
z-score = (x - m) / sd
x = raw score
m = mean
sd = standard deviation.
since m = 530 and sd = 180, the formula becomes:
z = (x - 530) / 180
when z is equal to .53, this formula becomes:
.53 = (x-530) / 180
solve for x to get x = 625.4
when x is equal to .52,this formula becomes:
.52 = (x-530) / 180
solve for x to get x = 623.60
the minimum score to get into college is going to be between 623.60 and 625.4
to be on the same side, figure 625.4
to be more exact, you can interpolate, or you would use a calculator that gives you the answer to more decimal places.
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:
z = .524400510
that corresponds to a raw score of:
.524400510 = (x - 530) / 180
solve for x to get:
x = 624.3920918
it's a matter of how close you need to get the answer.
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.
that ensures your score is greater than 70% of the population scores.
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