6. O points Muntrostate 1E 514 xp There are two major tests of readiness for col
ID: 3240473 • Letter: 6
Question
6. O points Muntrostate 1E 514 xp There are two major tests of readiness for college, the ACT and the SAT. ACT scores are reported on a scale from 1 to 36. The distribution of ACT scores for more than 1 million students in a recent high school graduating class was roughly normal with mean u- 20.8 and standard deviation o 4.8. SAT scores are reported on a scale from 400 to 1600. The SAT scores for 1.4 million students in the same graduating class were roughly normal with mean m 1026 and standard deviation a 209. How well must Abigail do on the SAT in order to place in the top 27% of all students? (Round your answer to the nearest whole number)Explanation / Answer
Solution:-
SAT scores are reported on a scale from 400 to 1600.
The SAT scores for 1.4 million students in the same graduating class were roughly normal with mean = 1026 and standard deviation = 209.
How well must Abigail do on the SAT in order to place in the top 27% of all students?
the mean is 1026 and the standard deviation is 209.
if she wants to be in the top 27% of all students, then she will have to have a score that is greater than or equal to the score of at least 73% of the students.
you would look in the z-score table for a z-score that has 73% or more of the area under the distribution curve to the left of it.
The cutoff z-score is 0.612813 since more than 73% of the z-scores would have areas under the normal distribution curve less than it. ( using online calculator for z calulator )
This means that less than 27% of the z-scores would have areas under the normal distribution curve greater than it.
You would then need to translate this z-score to a raw score.
the formula for z-score is:
z = (x-m)/s
z is the z-score
x is the raw score you are comparing against the mean.
m is the mean.
s is the standard deviation.
We know the following:
z = 0.612813
m = 1026
s = 209
the formula becomes:
0.612813 = (x - 1026) / 209
solve for x to get x = 0.612813 * 209 + 1026 = 1154.077917
she would have to get a SAT score greater than or equal to 1154.077917 or 1154 in order to be placed in the top 27% of the students taking the test.
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