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Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. The scores for the 500 students who took Ms. Johnson’s fina  Question banks Downloads My Bookmarks Reviews Important topics
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The scores for the 500 students who took Ms. Johnson’s fina [#permalink]
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Question Stats: 57% (02:13) correct 42% (01:32) wrong based on 94 sessions

The scores for the 500 students who took Ms. Johnson’s final exam have a normal distribution. There are 80 students who scored at least 92 points out of a possible 100 total points and 10 students who scored at or below 56.

 Quantity A Quantity B The average (arithmetic mean) score on the final exam 87

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: The scores for the 500 students who took Ms. Johnson’s fina [#permalink]
How should I proceed with this kind of qustions? Founder  Joined: 18 Apr 2015
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Re: The scores for the 500 students who took Ms. Johnson’s fina [#permalink]
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OE

Attachment: deviation.jpg [ 23.65 KiB | Viewed 6120 times ]

Quote:
Remember that a normal distribution curve has divisions of 34 percent, 14 percent, and 2 percent on each side of the mean. 80 out of 50 is 16 percent, or 14 percent + 2 percent, and 10 out of 500 is 2 percent. Draw a normal distribution curve and label it. There are three standard deviations between 92 and 56, so 92 - 56 = 36, and 36 ÷ 3 = 12. The mean is 92 - 12 = 80, which is smaller than Quantity B.

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Re: The scores for the 500 students who took Ms. Johnson’s fina [#permalink]
Ummm does that mean 2% of students scored (92+12)= 104 out of 100? ... I think there is something wrong with the question Intern Joined: 29 Jun 2018
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Re: The scores for the 500 students who took Ms. Johnson’s fina [#permalink]
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Let sd be the standard deviation, so 3 sd = (92 - 10) (Think why ?)

sd = 82 / 3

The average would be 92 -sd = 92 - (82/3) which would be less than 87
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Re: The scores for the 500 students who took Ms. Johnson’s fina [#permalink]
Carcass wrote:

The scores for the 500 students who took Ms. Johnson’s final exam have a normal distribution. There are 80 students who scored at least 92 points out of a possible 100 total points and 10 students who scored at or below 56.

 Quantity A Quantity B The average (arithmetic mean) score on the final exam 87

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Intern Joined: 15 May 2018
Posts: 38
Followers: 0

Kudos [?]: 5 , given: 1

Re: The scores for the 500 students who took Ms. Johnson’s fina [#permalink]
Carcass wrote:

The scores for the 500 students who took Ms. Johnson’s final exam have a normal distribution. There are 80 students who scored at least 92 points out of a possible 100 total points and 10 students who scored at or below 56.

 Quantity A Quantity B The average (arithmetic mean) score on the final exam 87

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given. Intern Joined: 27 Nov 2014
Posts: 30
Followers: 0

Kudos [?]: 4  , given: 0

Re: The scores for the 500 students who took Ms. Johnson’s fina [#permalink]
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Good One. M + SD = 92 and M - 2SD = 56, we need to find out M from here.
Intern Joined: 22 Apr 2019
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Re: The scores for the 500 students who took Ms. Johnson’s fina [#permalink]
Could you please elaborate the ans again? the given answer seems much abstruse.
Intern Joined: 25 May 2019
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Re: The scores for the 500 students who took Ms. Johnson’s fina [#permalink]
Can someone please explain how 16% (92 or more) is displayed in the bell curve at M+SD position? And why not at M-SD position (because this marks 16%)? GRE Instructor Joined: 10 Apr 2015
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Re: The scores for the 500 students who took Ms. Johnson’s fina [#permalink]
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Expert's post
Carcass wrote:

The scores for the 500 students who took Ms. Johnson’s final exam have a normal distribution. There are 80 students who scored at least 92 points out of a possible 100 total points and 10 students who scored at or below 56.

 Quantity A Quantity B The average (arithmetic mean) score on the final exam 87

-------ASIDE-----------------------------
A little extra background on standard deviations above and below the mean

If, for example, a set has a standard deviation of 4, then:
1 standard deviation = 4
2 standard deviations = 8
3 standard deviations = 12
1.5 standard deviations = 6
0.25 standard deviations = 1
etc

So, if the mean of a set is 9, and the standard deviation is 4, then:
2 standard deviations ABOVE the mean = 17 [since 9 + 2(4) = 17]
1.5 standard deviations BELOW the mean = 3 [since 9 - 1.5(4) = 3]
3 standard deviations ABOVE the mean = 21 [since 9 + 3(4) = 21]
etc.
-------------------------------------------------

We're told that 16% scored at least 92 points (80/500 = 10%)
When we examine the normal distribution curve, we see that 16% of all values are more than 1 standard deviation ABOVE the mean. So, we know that a test score of 92 points is 1 standard deviation ABOVE the mean.
So, if m = the mean of all the scores
and if d = the standard deviation of all the scores...
We can write: m + d = 92

We're also told that 2% scored less than 56 points (10/500 = 2%)
When we examine the normal distribution curve, we see that 2% of all values are more than 2 standard deviations BELOW the mean. So, we know that a test score of 56 points is 2 standard deviations BELOW the mean.
So, if m = the mean of all the scores
and if d = the standard deviation of all the scores...
We can write: m - 2d = 56

So, we now know two things:
m + d = 92
m - 2d = 56

Take the TOP equation, and multiply both sides by 2 to get:
2m + 2d = 184
m - 2d = 56

ADD the two equations to get: 3m = 240
Solve: m = 80

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com Founder  Joined: 18 Apr 2015
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Re: The scores for the 500 students who took Ms. Johnson’s fina [#permalink]
Expert's post
Thank you Sir for the stunning explanation.

Regards
_________________ Re: The scores for the 500 students who took Ms. Johnson’s fina   [#permalink] 27 May 2019, 16:11
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