Last visit was: 05 Nov 2024, 06:41 It is currently 05 Nov 2024, 06:41

Close

GRE Prep 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 GRE 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
User avatar
Retired Moderator
Joined: 07 Jun 2014
Posts: 4813
Own Kudos [?]: 11136 [7]
Given Kudos: 0
GRE 1: Q167 V156
WE:Business Development (Energy and Utilities)
Send PM
Most Helpful Community Reply
avatar
Director
Director
Joined: 09 Nov 2018
Posts: 505
Own Kudos [?]: 133 [11]
Given Kudos: 0
Send PM
General Discussion
avatar
Intern
Intern
Joined: 21 Jun 2018
Posts: 35
Own Kudos [?]: 14 [0]
Given Kudos: 0
Send PM
User avatar
Director
Director
Joined: 22 Jun 2019
Posts: 521
Own Kudos [?]: 706 [2]
Given Kudos: 161
Send PM
Re: On a particular test whose scores are distributed normally, [#permalink]
1
1
Bookmarks
sandy 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


Explanation:
The diagram below shows the standard distribution curve for any normally distributed variable. The percent figures correspond roughly to the standard percentiles both 1 and 2 standard deviations (SD) away from the mean: The 2nd percentile is 1,720, roughly corresponding to 2 standard deviations below the mean.

Therefore, the mean –2 standard deviations = 1,720.

Likewise, the 84th percentile is 1,990: 84% of a normally distributed set of data falls below the mean + 1 standard deviation, so the mean + 1 standard deviation = 1,990.

Call the mean M and the standard deviation S. Solve for these variables:
M – 2S = 1,720
M + S = 1,990

Subtract the first equation from the second equation:
3S = 270
S = 90

The question asks for the 16th percentile, which is the mean – 1 standard deviation or M – S. (It’s a fact to memorize that approximately 2% of normally distributed data falls below M – 2S, and approximately 14% of normally distributed data falls between M – 2S and M – S.)

Since M – 2S = 1,720, add another S to get M – S:
(M – 2S) + S = 1,720 + 90 = 1,810

Notice that the percentiles are not linearly spaced. The normal distribution is hump-shaped, so percentiles are bunched up around the hump and spread out farther away.

Attachment:
PERCENTILE.png
PERCENTILE.png [ 70.78 KiB | Viewed 9373 times ]
avatar
Manager
Manager
Joined: 10 Oct 2020
Posts: 113
Own Kudos [?]: 77 [0]
Given Kudos: 37
Send PM
Re: On a particular test whose scores are distributed normally, [#permalink]
1
1 standaed deivation below the mean, so it is 16th percentile

so, If 1 SD below the mean leads to 16th percentile
so, SD for 15th ppercentile < 1 SD => 15/16 = 0.94
Now,
M - 0.94 X SD = 1900 - 0.94 X 90 = 1815.40, it is close to D
User avatar
GRE Prep Club Legend
GRE Prep Club Legend
Joined: 07 Jan 2021
Posts: 5006
Own Kudos [?]: 74 [0]
Given Kudos: 0
Send PM
Re: On a particular test whose scores are distributed normally, [#permalink]
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Prep Club for GRE Bot
Re: On a particular test whose scores are distributed normally, [#permalink]
Moderators:
GRE Instructor
77 posts
GRE Forum Moderator
37 posts
Moderator
1111 posts
GRE Instructor
228 posts

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