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The average (arithmetic mean) of a normal distribution of a

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The average (arithmetic mean) of a normal distribution of a [#permalink] New post 16 Aug 2010, 10:25
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26% (01:16) correct 74% (00:48) wrong based on 31 sessions
The average (arithmetic mean) of a normal distribution of a school's test scores is 65, and standard deviation of the distribution is 6.5. A student scoring a 78 on the exam is in what percentile of the school?

A. 63rd
B. 68th
C. 84th
D. 96th
E. 98th
[Reveal] Spoiler: OA

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Re: Statistics question [#permalink] New post 16 Aug 2010, 10:50
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aiming4mba wrote:
The average (arithmetic mean) of a normal distribution of a school's test scores is 65, and standard deviation of the distribution is 6.5. A student scoring a 78 on the exam is in what percentile of the school?

a.63rd
b.68th
c.84th
d.96th
e.98th


You can solve this question if you know the 68.2-95.4-99.7 rule of normal distributions (though the normal distribution is an absolutely continuous probability distribution and this is not the case in the question): 78 is 2 SD from the mean (65+2*6.5=78), so below it are 95.4+\frac{100-95.4}{2}=97.7\approx{98} percent of data points, answer E. But don't worry about this question, normal distribution IS NOT tested on GMAT and you don't have to know this rule.
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Percentile --normal distribution [#permalink] New post 06 Feb 2011, 19:32
The average (arithmetic mean) of a normal distribution of a school's test scores is 65, and standard deviation of the distribution is 6.5. A student scoring a 78 on the exam is in what percentile of the school?

A
63rd percentile
B
68th percentile
C
84th percentile
D
96th percentile
E
98th percentile
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Re: Statistics question [#permalink] New post 18 May 2011, 22:33
50 + 34 + 14 = 98%

2 sigma ahead of average.
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Re: Statistics question [#permalink] New post 19 May 2011, 20:17
50 + 34 + 14 = 98 hence E
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Re: The average (arithmetic mean) of a normal distribution of a [#permalink] New post 07 Dec 2012, 10:57
Bunuel wrote:
But don't worry about this question, normal distribution IS NOT tested on GMAT and you don't have to know this rule.

Bueuel,
so they will not test on such problems in GMAT?

also how did you arrive at the answer? more hand holding please.
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Re: The average (arithmetic mean) of a normal distribution of a [#permalink] New post 07 Dec 2012, 12:19
Unfortunately or not, i have seen this question on Grockit. Its strange they are throwing such questions that do not have possibilities of being tested on the actual test.
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Re: The average (arithmetic mean) of a normal distribution of a [#permalink] New post 08 Dec 2012, 05:06
Expert's post
Simba2012 wrote:
Bunuel wrote:
But don't worry about this question, normal distribution IS NOT tested on GMAT and you don't have to know this rule.

Bueuel,
so they will not test on such problems in GMAT?

also how did you arrive at the answer? more hand holding please.


Yes, normal distribution (and its 68.2-95.4-99.7 rule) is not tested on the GMAT.
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The average (arithmetic mean) of a normal distribution of a [#permalink] New post 04 Jun 2013, 09:52
The average (arithmetic mean) of a normal distribution of a school's test scores is 65, and standard deviation of the distribution is 6.5. A student scoring a 78 on the exam is in what percentile of the school?
A)63th percentile
B)68th percentile
C)84th percentile
D)96th percentile
E)98th percentile
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Re: The average (arithmetic mean) of a normal distribution of a [#permalink] New post 04 Jun 2013, 12:26
Stiv wrote:
The average (arithmetic mean) of a normal distribution of a school's test scores is 65, and standard deviation of the distribution is 6.5. A student scoring a 78 on the exam is in what percentile of the school?
A)63th percentile
B)68th percentile
C)84th percentile
D)96th percentile
E)98th percentile



E...since the distribution of the curve is 2%,14%,34%,34%,14%,2%
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Re: The average (arithmetic mean) of a normal distribution of a [#permalink] New post 04 Jun 2013, 14:16
Expert's post
Stiv wrote:
The average (arithmetic mean) of a normal distribution of a school's test scores is 65, and standard deviation of the distribution is 6.5. A student scoring a 78 on the exam is in what percentile of the school?
A)63th percentile
B)68th percentile
C)84th percentile
D)96th percentile
E)98th percentile


Merging similar topics.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: The average (arithmetic mean) of a normal distribution of a [#permalink] New post 04 Jun 2013, 20:48
Expert's post
Stiv wrote:
The average (arithmetic mean) of a normal distribution of a school's test scores is 65, and standard deviation of the distribution is 6.5. A student scoring a 78 on the exam is in what percentile of the school?
A)63th percentile
B)68th percentile
C)84th percentile
D)96th percentile
E)98th percentile


This particular question is out of scope.

Note that mean and SD are tested on the GMAT but normal distributions are not. Then again, a question could mention that scores are normally distributed - the reason for that is that SD concept may not make sense for some distributions e.g. distributions with too much negative skewness etc. Hence they might mention that it is normally distributed for the discerning statistician. Normally, it can just be ignored. Focus only on the SD concepts. e.g. they could ask - which scores are 3 SD away from the mean?
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Re: The average (arithmetic mean) of a normal distribution of a   [#permalink] 04 Jun 2013, 20:48
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