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Difficulty:
45%
(medium)
Question Stats:
68%
(02:18)
correct 32%
(02:11)
wrong
based on 19
sessions
History
Date
Time
Result
Not Attempted Yet
sabrinaZ
In a normal distribution, 68% of the scores lie within one standard deviation of the mean. If the SAT scores of all the high school juniors in Center City followed a normal distribution with a mean of 500 and a standard deviation of 100, and if 10,200 students scored between 400 and 500, approximately how many students scored above 600?
A. 2,400 B. 4,800 C. 5,100 D. 7,200 E. 9,600
Show more
Please refer to the diagram below for the normal distribution.
50% lies below the mean. Also since 68% lies between 1 standard deviation, 34% lies below the mean and 34% lies above the mean.
Those who scored between 400 and 500 is 34% of the students = 10,200
So, \(\frac{34}{100} * Total \space Students = 10200\)
Total Students = \(\frac{100}{34} * 10200 = 30000\)
1 standard deviation above the mean = 500 + 100 = 600. So 50 + 34 = 84% lies up to 1 standard deviation above the mean.
The remaining is 16%. Therefore the number of students = 16% of 30000 = 4800
Option B
Arun Kumar
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In a normal distribution, 68% of the scores lie within one standard deviation of the mean. If the SAT scores of all the high school juniors in Center City followed a normal distribution with a mean of 500 and a standard deviation of 100, and if 10,200 students scored between 400 and 500, approximately how many students scored above 600?
Show more
You do not need to know a thing about "normal distributions" for the GMAT, so if a question were to ask about them, it would need to tell you, within the question itself, everything you need to know about them. This question does not do that, and it's unanswerable as written (unless you bring to it outside knowledge about normal distributions). The "normal distribution" is an infinite distribution, so this question is flawed from the outset - the best it can say is that this finite set is "approximately normal". But the crucial piece of information the question is missing is that normal distributions are symmetric. Without that information, you can't do anything here.
Since an approximately normal distribution is symmetric, of the 68% of values within one standard deviation of the mean, 34% will be above the mean, and 34% will be below the mean (assuming no values equal the mean, which is something very likely to be true of the SAT scores in this question, another grievous error in the question design). So here, at least guessing what the question intends, 10,200 represents 34% of all test scores. Further, if 68% of scores are within one standard deviation of the mean, the rest, or 32%, are more than one standard deviation away from the mean. Since a normal distribution is symmetric, half of those, or 16%, will be more than one standard deviation above the mean.
We know 10,200 represents 34% of all values, and we're trying to find what number represents 16% of all values, so the answer is just (16/34)(10,200), which is clearly less than half of 10,200, but not by much, so 4800 will be correct.
But this is a very badly conceived problem, and is not something the GMAT could ever ask. What is the source?
This Question is Locked Due to Poor Quality
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