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A Bell Curve (Normal Distribution) has a mean of − 1 and a standard  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 55% (01:14) correct 45% (01:19) wrong based on 269 sessions

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A Bell Curve (Normal Distribution) has a mean of − 1 and a standard deviation of 1/8 . How many integer values are within three standard deviations of the mean?

A. 0
B. 1
C. 3
D. 6
E. 7

Originally posted by hemanthp on 26 Sep 2010, 09:53.
Last edited by hemanthp on 29 Sep 2010, 22:17, edited 1 time in total.
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Re: A Bell Curve (Normal Distribution) has a mean of − 1 and a standard  [#permalink]

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hemanthp wrote:
A Bell Curve (Normal Distribution) has a mean of − 1 and a standard deviation [highlight]of .[/highlight] How many integer values are within three standard deviations of the mean?

0
1
3
6
7

Like this? +1 please!

To answer this question a) the standard deviation is required b) the list of elements in the set is required.

If these inputs are available then the number of integer values present within the S.D can be found

a) First standard deviation of the mean can be found by finding the number of elements of the set that are in the range - (Mean-S.D, Mean+S.D)

b) First standard deviation of the mean can be found by finding the number of elements of the set that are in the range -
(Mean-2*S.D, Mean+2*S.D)

c) First standard deviation of the mean can be found by finding the number of elements of the set that are in the range - (Mean-3*S.D, Mean+3*S.D)
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Re: A Bell Curve (Normal Distribution) has a mean of − 1 and a standard  [#permalink]

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2
Guys... Sorry about missing the 1/8. This is from KAPLAN CATs. I liked the question. Kudos me if you like the OQ, OA and OE:
Choice (B) is correct; to be within three standard deviations of the mean means to be within 3*(1/8) = 0.375 of the mean. The mean is - 1, so to be within 0.375 of - 1 means to be greater than - 1 - 0.375 = - 1.375 and less than - 1 + 0.375 = - 0.625. The only integer within (three standard deviations) of the mean, i.e., the only integer in the interval - 1.375 to - 0.625, where the endpoints - 1.375 and - 0.625 are not included, is the mean itself, - 1.

Choice (A) is incorrect; it might arise from the thinking that 3/8 isn't big enough to get to another integer, and so the answer would be 0.

Choice (B) is correct, as stated above.

Choice (C) is wrong; it might come from incorrectly associating 3 standard deviations with the number 3 as an answer. Also, the student might incorrectly believe that all Bell Curves have the standard Normal distribution, with a mean of 0 and a standard deviation of 1. Thus, 3 times a standard deviation of 1 might suggest an answer of 3.

Choice (D) is wrong; the student might incorrectly believe that all Bell Curves have the standard Normal distribution. Thus, three standard deviations on each side of the mean, might suggest an answer of 6.

Choice (E) is wrong; this is the number of integers in the interval (including the endpoints) from – 3 to +3. The student might incorrectly believe that all Bell Curves have the standard Normal distribution. Thus, three standard deviations of 1 from the mean 0 might suggest an answer of 7 integers in the interval from - 3 to 3, when the endpoints - 3 and 3 are included.
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Re: A Bell Curve (Normal Distribution) has a mean of − 1 and a standard  [#permalink]

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Got the question correctly -- the second item -- [highlight]b) the list of elements in the set is required.[/highlight] is not required.

With the new information, there is only one integer value (-1) that is between (-1.375, -0.625) i.e., falls within the three 3 SD range.
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GMAT 1: 800 Q51 V51 A bell curve (Normal Distribution) has a mean of -1 and a standard de  [#permalink]

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A bell curve (Normal Distribution) has a mean of -1 and a standard deviation of 1/8.
How many integer values are within three standard deviation of mean?

a)1
b)2
c)3
d)4
e)5

Please assist with above problem.
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Re: A bell curve (Normal Distribution) has a mean of -1 and a standard de  [#permalink]

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Top Contributor
alanforde800Maximus wrote:
A bell curve (Normal Distribution) has a mean of -1 and a standard deviation of 1/8.
How many integer values are within three standard deviation of mean?

a)1
b)2
c)3
d)4
e)5

Please assist with above problem.

Mean = -1
Standard Deviation = 1/8

1 unit of standard deviation BELOW the mean = -1 - 1/8 = -1 1/8
2 units of standard deviation BELOW the mean = -1 - 1/8 - 1/8 = -1 2/8
2 units of standard deviation BELOW the mean = -1 - 1/8 - 1/8 - 1/8 = -1 3/8

1 unit of standard deviation ABOVE the mean = -1 + 1/8 = -7/8
2 units of standard deviation ABOVE the mean = -1 + 1/8 + 1/8= -6/8
3 units of standard deviation ABOVE the mean = -1 + 1/8 + 1/8 + 1/8= -5/8

So, all values from -1 3/8 to -5/8 are within 3 standard deviations of the mean.

Within this range, there is only 1 integer value: -1

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Re: A Bell Curve (Normal Distribution) has a mean of − 1 and a standard  [#permalink]

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Can someone elaborate on this question?

How am I able to know how many integer values are withing 3 units of standard deviation without knowing the set of values that have itself?
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Re: A Bell Curve (Normal Distribution) has a mean of − 1 and a standard  [#permalink]

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Can someone elaborate on this question?

How am I able to know how many integer values are withing 3 units of standard deviation without knowing the set of values that have itself?
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Re: A Bell Curve (Normal Distribution) has a mean of − 1 and a standard  [#permalink]

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_________________ Re: A Bell Curve (Normal Distribution) has a mean of − 1 and a standard   [#permalink] 01 Oct 2018, 04:52
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