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

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pmFollowed by: 1 member

by BTGModeratorVI » Wed Jan 06, 2021 8:09 am

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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

Answer: B
Source: Kaplan

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Re: A Bell Curve (Normal Distribution) has a mean of -1 and a standard deviation of 1/8 . How many integer values are wi

by Scott@TargetTestPrep » Fri Jan 15, 2021 9:14 am

BTGModeratorVI wrote: ↑
Wed Jan 06, 2021 8:09 am
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

Answer: B

Solution:

The minimum value that falls within 3 standard deviations is -1 - 3 x 1/8 = -1 ⅜ and the maximum value that falls with 3 standard deviations is -1 + 3 x 1/8 = -⅝. We see that there is only one integer that falls between -1 ⅜ and -⅝, namely -1.

Answer: B

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Founder and CEO
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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

Re: A Bell Curve (Normal Distribution) has a mean of -1 and a standard deviation of 1/8 . How many integer values are wi

by Brent@GMATPrepNow » Sat Jan 16, 2021 6:51 am

BTGModeratorVI wrote: ↑
Wed Jan 06, 2021 8:09 am
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

Answer: B
Source: Kaplan

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

Brent Hanneson - Creator of GMATPrepNow.com

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