A Bell Curve (Normal Distribution) has a mean of âˆ’ 1

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gmat_winter: Senior | Next Rank: 100 Posts; Posts: 34; Joined: Tue Oct 14, 2014 8:23 am; Thanked: 1 times

by gmat_winter » Wed Apr 01, 2015 6:04 am

A Bell Curve (Normal Distribution) has a mean of âˆ’ 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

Source Kaplan ; Is there a way I can make an estimation and get the answer correct instead of dividing 3/8 ?

OAB

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Source: Beat The GMAT — Problem Solving | Wed Apr 01, 2015 6:04 am

DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members; Location: Boston, MA; Thanked: 1153 times; GMAT Score:770

by DavidG@VeritasPrep » Wed Apr 01, 2015 6:19 am

It's enough to see that three standard deviations will be less than one. (3 * 1/8 = 3/8)

So three standard deviations below -1 would be -1 - (3/8) This will be between -1 and -2, and doesn't encompass a new integer.

Three standard deviations above -1 would be -1 + (3/8) This will be between -1 and 0, and doesn't encompass a new integer.

-1 will be the only integer in the range.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Apr 01, 2015 8:29 am

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.

In the stated questions, we're asked to find values that are within 3 standard deviations of the mean
So, as David has demonstrated, we need to determine 3 standard deviations above the mean AND 3 standard deviations below the mean

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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jain2016: Master | Next Rank: 500 Posts; Posts: 313; Joined: Tue Oct 13, 2015 7:01 am; Thanked: 2 times

by jain2016 » Thu Feb 11, 2016 9:56 am

Brent@GMATPrepNow wrote: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.

In the stated questions, we're asked to find values that are within 3 standard deviations of the mean
So, as David has demonstrated, we need to determine 3 standard deviations above the mean AND 3 standard deviations below the mean

Cheers,
Brent

Hi Brent ,

3 Standard deviation above the mean = -5/8 [since -1 + 3/8 = -5/8]

3 standard deviation below the mean = -11/8 [since -1 - 3/8 = -11/8]

Now what will be the next step?

Please advise.

Many thanks in advance.

SJ

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Feb 11, 2016 10:14 am

jain2016 wrote: Hi Brent ,

3 Standard deviation above the mean = -5/8 [since -1 + 3/8 = -5/8]

3 standard deviation below the mean = -11/8 [since -1 - 3/8 = -11/8]

Now what will be the next step?

Please advise.

Many thanks in advance.

SJ

Great. The question asks us to determine how many INTEGERS are between -5/8 and -11/8
There is only ONE integer between these values (that integer is -1).
So, the correct answer is B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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by Matt@VeritasPrep » Thu Feb 11, 2016 5:40 pm

jain2016 wrote: Hi Brent ,

3 Standard deviation above the mean = -5/8 [since -1 + 3/8 = -5/8]

3 standard deviation below the mean = -11/8 [since -1 - 3/8 = -11/8]

Now what will be the next step?

Please advise.

Many thanks in advance.

SJ

You'd then have

-11/8 < integer < -5/8

and look for the integer(s) that fall in that range. In this case, only -1 does, so there's one and only one integer value.

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