A Bell Curve (Normal Distribution) has a mean of − 1 and a standard

Question

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

BrentGMATPrepNow · Accepted Answer

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

Answer: B

ezhilkumarank · Answer

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)

hemanthp · Answer

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.

ezhilkumarank · Answer

Got the question correctly -- the second item --  b) the list of elements in the set is required.  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.

Zoser · Answer

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?

bv8562 · Answer

Given:
Mean = -1
S.D = 1/8

"Values within three standard deviations of the mean" means the following:

m+3d and m-3d; where d = standard deviation

Therefore, 
m+3d = -1+3/8 = -5/8 = -0.6
m-3d = -1-3/8 = -11/8 = -1.37

Between, -1.37 and -0.6 we have -1 as an integer value. Hence, answer is option B.

IanStewart · Answer

As Zoser above was saying, this question makes no sense. If a question says "a list has a mean of -1 and a standard deviation of 1/8, how many integer values are within 3 standard deviations of the mean?" that question does not mean "how many integers are between -1 - 3/8 and -1 + 3/8" (or between -1.375 and -0.625). It means "how many values in the set or distribution are integers that are between -1.375 and -0.625?". So if our set is

-9/8, -9/8, -9/8, -7/8, -7/8, -7/8

the answer would be 'zero', and if the set were instead

-1.25, -1, -1, -1, -1, -1, -1, -0.75

the answer would be 'six', because six values (all of the values equal to -1) are between -1.375 and -0.625.

So we need to know about our list or set to answer this question. And you don't need to know anything at all about "normal distributions" on the GMAT, but if you do know about those distributions, you'll know they're infinite continuous distributions. And in a continuous distribution, the number of values in the distribution equal to any one specific number is zero. So that's the answer a statistician would give here, but that statistician would be using knowledge miles beyond the scope of the GMAT.

The question writer means to ask "how many distinct integers are there between -1.375 and -0.625", and the answer to that question is 'one', but that's not what this question is actually asking.

Posted from my mobile device

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A Bell Curve (Normal Distribution) has a mean of − 1 and a standard

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