A certain characterstic in a large population has a : PS Archive
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 07 Dec 2016, 14:32

# Chicago-Booth

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A certain characterstic in a large population has a

Author Message
Manager
Joined: 31 Dec 2003
Posts: 214
Location: US
Followers: 0

Kudos [?]: 30 [0], given: 0

A certain characterstic in a large population has a [#permalink]

### Show Tags

08 Sep 2004, 03:39
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

A certain characterstic in a large population has a distribution that is symmetric about the mean M. If 68 percent of the distribution lies within one standard deviation D of the mean, what percent of the distribution is less than M+D?
A. 16% B.32% C. 48% D. 84% E. 92%

Thanks.
Manager
Joined: 05 Sep 2004
Posts: 97
Followers: 1

Kudos [?]: 3 [0], given: 0

### Show Tags

08 Sep 2004, 09:14
That's just your straight normal distribution.

Symmetry=> 50% of the distribution lies above the mean (M) and 50% below

If 68% lies within 1 s.d. (D) of M, then 34% lies within +1 D and 34% lies within -1 D.

Thus, the distribution below M+D is the same as the complement of the distribution above M+D, or 1- 0.16 = 0.84.

Alternatively, the distribution below can be found as the sum of the distributions b/w M and +D (34%), M and -D (34%), and below -D (16%), which also sums to 84%.

Director
Joined: 16 Jun 2004
Posts: 893
Followers: 3

Kudos [?]: 56 [0], given: 0

### Show Tags

08 Sep 2004, 09:59
Illustrated below for easier understanding..
Attachments

SD.JPG [ 32.94 KiB | Viewed 686 times ]

Last edited by venksune on 08 Sep 2004, 12:52, edited 1 time in total.
Joined: 31 Dec 1969
Location: Russian Federation
Concentration: Entrepreneurship, Technology
GMAT 1: 710 Q49 V0
GMAT 2: 700 Q V
GMAT 3: 740 Q40 V50
GMAT 4: 700 Q48 V38
GMAT 5: 710 Q45 V41
GMAT 6: 680 Q47 V36
GMAT 7: Q42 V44
GMAT 8: Q42 V44
GMAT 9: 740 Q49 V42
GMAT 10: 740 Q V
GMAT 11: 500 Q47 V33
GMAT 12: 670 Q V
WE: Engineering (Manufacturing)
Followers: 0

Kudos [?]: 196 [0], given: 100936

### Show Tags

08 Sep 2004, 10:43
A certain characterstic in a large population has a distribution that is symmetric about the mean M. If 68 percent of the distribution lies within one standard deviation D of the mean, what percent of the distribution is less than M+D?
A. 16% B.32% C. 48% D. 84% E. 92%

If we could draw a normal bell shaped distribution, we could make the explanation clearer.

In the absence of the normal distribution let me improvise it with this dotted line

A-------- (M-D)----------M------------(M +D)-----------B
In this diagram M is the mean D represents the length of a deviation
This implies that (M-D) to (M+D) represents distribution lying within one standard deviation of the mean and this is 68%
The distribution lying within A to (M-D) and that lying between (M+D) to B must equally account for the remaining 32% (100-68) of the disdtribituion
Thus each of these points will have 16% of the distribution

So we have
A to (M-D) = 16%
(M-D) to M +D =68%
(M+D) to B = 16%

We are intereted in distribution less than (M+D) ie the distribution from A to (M +D) = 16% + 68% = 84%

I hope this help
Manager
Joined: 31 Dec 2003
Posts: 214
Location: US
Followers: 0

Kudos [?]: 30 [0], given: 0

### Show Tags

08 Sep 2004, 23:23
Thanks everyone. I understand now.
Venksune,
This distribution - 68% , 95% and 99% will hold true only for a normal distribution is it. Is there any other concept similar to this in SD and distributions.
Thanks.
Display posts from previous: Sort by