It is currently 11 Dec 2017, 21:57

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

On a particular test whose scores are distributed normally, the 2nd pe

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Top Contributor
Senior RC Moderator
User avatar
P
Status: It always seems impossible until it's done!!
Joined: 29 Aug 2012
Posts: 1063

Kudos [?]: 1597 [0], given: 281

Location: India
GMAT 1: 680 Q47 V34
WE: General Management (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
On a particular test whose scores are distributed normally, the 2nd pe [#permalink]

Show Tags

New post 25 Oct 2017, 11:07
Top Contributor
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

27% (01:13) correct 73% (02:34) wrong based on 22 sessions

HideShow timer Statistics

On a particular test whose scores are distributed normally, the 2nd percentile is 1,720, while the 84th percentile is 1,990. What score, rounded to the nearest 10, most closely corresponds to the 16th percentile?

(A) 1,750
(B) 1,770
(C) 1,790
(D) 1,810
(E) 1,830
[Reveal] Spoiler: OA

_________________

Become a GMAT Club Premium member to avail lot of discounts

Kudos [?]: 1597 [0], given: 281

2 KUDOS received
VP
VP
avatar
P
Joined: 22 May 2016
Posts: 1108

Kudos [?]: 397 [2], given: 640

On a particular test whose scores are distributed normally, the 2nd pe [#permalink]

Show Tags

New post 25 Oct 2017, 11:54
2
This post received
KUDOS
2
This post was
BOOKMARKED
Gnpth wrote:
On a particular test whose scores are distributed normally, the 2nd percentile is 1,720, while the 84th percentile is 1,990. What score, rounded to the nearest 10, most closely corresponds to the 16th percentile?

(A) 1,750
(B) 1,770
(C) 1,790
(D) 1,810
(E) 1,830

Attachment:
normdist.png
normdist.png [ 13.13 KiB | Viewed 344 times ]

Answer
Quickly sketch a normal distribution: 0 ----2----16----50----84----96----100

A score at 84th percentile is three standard deviations away from a score at 2nd percentile

1,990 - 1,720 = 270

\(\frac{270}{3 SDs}\) = 90 = one SD

16th percentile score is +1 SD greater than 2nd percentile score
16th percentile score would be:
1,720 + 90 = 1810

ANSWER D

Explanation
Data is clustered around the mean, and percent distributed in any segment has a fixed number

"Distributed normally" means the data fall into the normal distribution curve, the top figure in the diagram.
68 percent of the data fall within one standard deviation from the mean -- one deviation above, one deviation below (so 34%/34%)

The percent of data underneath any part of the curve always follows the distribution seen in the top figure (figures in green ink):
2 (percent of the data), then 14 (percent of data) , then 34, 34, 14, 2

If you memorize those numbers and start with 50 as the mean, just add to get percentiles:
RIGHT OF THE MEAN: (50+34) = 84 | (84+14) = 98 | (98+2) = 100
LEFT OF THE MEAN: (50-34) = 16 | (16-14) = 2 | (2-2) = 0

Standard deviation corresponds with percentiles in a normal distribution
See middle figure, that pattern will always hold:
0th percentile is -3 SDs from mean
2nd percentile is -2 SDs from mean
. . .
84th percentile is + 1 SD from mean
100th percentile is +3 SDs from mean

What is score at 16th percentile here?

Score at 2nd percentile = 1,720
Score at 84th percentils = 1990

Score at the 16th percentile?

The score at the 84th percentile is THREE standard deviations from the score at the 2nd percentile (just count segments)

Find the difference between the scores
Divide by 3 (for three standard deviations)

(1,990 - 1,720) = 270

\(\frac{270}{3SDs}\) = 90

So 90 = ONE standard deviation

The 16th percentile is +1 SD away from the 2nd percentile (see top and middle figures)

So, 16th percentile score = the given 2nd percentile score (1,720) + ONE standard deviation (90)

1,720 + 90 = 1810

ANSWER D

Kudos [?]: 397 [2], given: 640

On a particular test whose scores are distributed normally, the 2nd pe   [#permalink] 25 Oct 2017, 11:54
Display posts from previous: Sort by

On a particular test whose scores are distributed normally, the 2nd pe

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.