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A bell curve (Normal Distribution) has a mean of -1 and a s

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by Brent@GMATPrepNow » Mon Sep 26, 2016 12:36 pm
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
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: A

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by Matt@VeritasPrep » Thu Sep 29, 2016 7:09 pm
Let's do it algebraically, with m = mean and d = standard deviation:

m - 3*d < our numbers < m + 3*d

-1 - 3*(1/8) < our numbers < -1 + 3*(1/8)

-11/8 < our numbers < -5/8

So our numbers are anything greater than -11/8 and less than -5/8. The only integer like that is -1, so there's ONE such integer, and the answer is A.
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by Matt@VeritasPrep » Thu Sep 29, 2016 7:10 pm
Another approach would be noticing that we need to go at least eight (!) standard deviations in either direction just to get to another integer. (For instance, -1 + 8*(1/8) gets us to 0.)

Since we aren't going that far, we won't get any other integers, and we'll only have the one we started with: -1.
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