It is currently 12 Dec 2017, 03:37

### 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

# Three fair coins are labeled with a zero (0) on one side and

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

### Hide Tags

Manager
Joined: 01 Nov 2007
Posts: 147

Kudos [?]: 451 [5], given: 0

Three fair coins are labeled with a zero (0) on one side and [#permalink]

### Show Tags

17 Jan 2008, 10:02
5
KUDOS
13
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

41% (02:17) correct 59% (01:51) wrong based on 211 sessions

### HideShow timer Statistics

Three fair coins are labeled with a zero (0) on one side and a one (1) on the other side. Jimmy flips all three coins at once and computes the sum of the numbers displayed. He does this over 1000 times, writing down the sums in a long list. What is the expected standard deviation of the sums on this list?
(A) 1/2
(B) 3/4
(C)$$\sqrt{3}$$/2
(D)$$\sqrt{5}$$/2
(E) 5/4

[Reveal] Spoiler:
I don't know how to solve this question. Please provide full explanation.

Thanks
[Reveal] Spoiler: OA

Last edited by Vyshak on 30 Jul 2016, 22:28, edited 2 times in total.
Formatted and added OA

Kudos [?]: 451 [5], given: 0

Director
Joined: 01 Jan 2008
Posts: 617

Kudos [?]: 207 [5], given: 1

Re: Three fair coins are labeled with a zero (0) on one side and [#permalink]

### Show Tags

17 Jan 2008, 15:47
5
KUDOS
2
This post was
BOOKMARKED
variance of binomial distribution is n*p*(1-p), n = 3, p = 1/2

variance = 3*1/2*(1-1/2)= 3/4

stdev = sqrt(variance) = sqrt(3)/2

After many trials sample standard deviation is close to theoretical standard deviation = sqrt(3)/2.

C is the answer.

Kudos [?]: 207 [5], given: 1

CEO
Joined: 17 Nov 2007
Posts: 3583

Kudos [?]: 4712 [3], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Re: Three fair coins are labeled with a zero (0) on one side and [#permalink]

### Show Tags

17 Jan 2008, 10:11
3
KUDOS
Expert's post
2
This post was
BOOKMARKED
C

$$\sigma=\sqrt{\frac{\sum(x-x_a)^2}{n}}$$

where, $$x$$ - the sum of 3 numbers
$$x_a$$ - the average sum.

probabilities for $$x$$:
$$x=0:$$ $$p_0=\frac18;$$ $$x=1:$$ $$p_1=\frac38;$$ $$x=2:$$ $$p_2=\frac38;$$ $$x=3:$$ $$p_3=\frac18$$

$$x_a=\frac32$$

$$n \to \infty$$ (n=1000 is very large number)

we can write:

$$\sigma=\sqrt{\frac18*(0-\frac32)^2+\frac38*(1-\frac32)^2+\frac38*(2-\frac32)^2+\frac18*(3-\frac32)^2}$$

$$\sigma=\sqrt{\frac18*\frac94+\frac38*\frac14+\frac38*\frac14+\frac18*\frac94}$$

$$\sigma=\sqrt{\frac{24}{32}}=\sqrt{\frac34}=\frac{\sqrt3}{2}$$

good Q +1
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

Kudos [?]: 4712 [3], given: 360

Manager
Joined: 15 Jul 2008
Posts: 205

Kudos [?]: 74 [1], given: 0

Re: Three fair coins are labeled with a zero (0) on one side and [#permalink]

### Show Tags

04 Sep 2008, 08:16
1
KUDOS
1
This post was
BOOKMARKED
walker wrote:
C

$$\sigma=\sqrt{\frac{\sum(x-x_a)^2}{n}}$$

where, $$x$$ - the sum of 3 numbers
$$x_a$$ - the average sum.

probabilities for $$x$$:
$$x=0:$$ $$p_0=\frac18;$$ $$x=1:$$ $$p_1=\frac38;$$ $$x=2:$$ $$p_2=\frac38;$$ $$x=3:$$ $$p_3=\frac18$$

$$x_a=\frac32$$

$$n \to \infty$$ (n=1000 is very large number)

we can write:

$$\sigma=\sqrt{\frac18*(0-\frac32)^2+\frac38*(1-\frac32)^2+\frac38*(2-\frac32)^2+\frac18*(3-\frac32)^2}$$

$$\sigma=\sqrt{\frac18*\frac94+\frac38*\frac14+\frac38*\frac14+\frac18*\frac94}$$

$$\sigma=\sqrt{\frac{24}{32}}=\sqrt{\frac34}=\frac{\sqrt3}{2}$$

good Q +1

Walker, can you point out the flaw in my approach. I know from binomial dist parameters that my approach is wrong... but i have forgotten why this approach is worng.

For the trial, prob mass funtion for all outcomes = 1/2
so E[x] = 0*1/2 + 1*1/2 ... first moment
E[x^2] = 0^2 * 1/2 + 1^2 *1/2 ... second moment

E[x^2] - (E[x])^2 = 1/4 ... second central moment = var[x]

SD = sqrt(var[x]) = 1/sqrt(x)..

Kudos [?]: 74 [1], given: 0

CEO
Joined: 17 Nov 2007
Posts: 3583

Kudos [?]: 4712 [1], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Re: Three fair coins are labeled with a zero (0) on one side and [#permalink]

### Show Tags

04 Sep 2008, 11:02
1
KUDOS
Expert's post
bhushangiri wrote:
Walker, can you point out the flaw in my approach. I know from binomial dist parameters that my approach is wrong... but i have forgotten why this approach is worng.

I did not dig deep, but maybe you forgot that x is "the sum of the numbers" and E(x)=3C0*0*1/2^3+3C1*1*1/2^3+3C2*2*1/2^3+3C3*3*1/2^3=0+3/8+6/8+3/8=12/8=3/2
E(x^2)=3C0*0*1/2^3+3C1*1*1/2^3+3C2*4*1/2^3+3C3*9*1/2^3=0+3/8+12/8+9/8=24/8=3
var[x]=E[x^2] - (E[x])^2=3-(3/2)^2=3/4

SD = sqrt(var[x]) = $$\frac{sqrt{3}}{2}$$
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

Kudos [?]: 4712 [1], given: 360

Math Expert
Joined: 02 Sep 2009
Posts: 42560

Kudos [?]: 135317 [1], given: 12686

Re: Three fair coins are labeled with a zero (0) on one side and [#permalink]

### Show Tags

12 May 2017, 10:50
1
KUDOS
Expert's post
BrushMyQuant wrote:
Bunuel: Isn't this out of scope for GMAT?
JCLEONES wrote:
Three fair coins are labeled with a zero (0) on one side and a one (1) on the other side. Jimmy flips all three coins at once and computes the sum of the numbers displayed. He does this over 1000 times, writing down the sums in a long list. What is the expected standard deviation of the sums on this list?
(A) 1/2
(B) 3/4
(C)$$\sqrt{3}$$/2
(D)$$\sqrt{5}$$/2
(E) 5/4

[Reveal] Spoiler:
I don't know how to solve this question. Please provide full explanation.

Thanks

Yes, it's out of scope. So, you can ignore it and move on.
_________________

Kudos [?]: 135317 [1], given: 12686

Manager
Joined: 01 Nov 2007
Posts: 147

Kudos [?]: 451 [0], given: 0

Re: Three fair coins are labeled with a zero (0) on one side and [#permalink]

### Show Tags

17 Jan 2008, 11:14
That´s a difficult solution. +1
Any other approach?

walker wrote:
C

$$\sigma=\sqrt{\frac{\sum(x-x_a)^2}{n}}$$

where, $$x$$ - the sum of 3 numbers
$$x_a$$ - the average sum.

probabilities for $$x$$:
$$x=0:$$ $$p_0=\frac18;$$ $$x=1:$$ $$p_1=\frac38;$$ $$x=2:$$ $$p_2=\frac38;$$ $$x=3:$$ $$p_3=\frac18$$

$$x_a=\frac32$$

$$n \to \infty$$ (n=1000 is very large number)

we can write:

$$\sigma=\sqrt{\frac18*(0-\frac32)^2+\frac38*(1-\frac32)^2+\frac38*(2-\frac32)^2+\frac18*(3-\frac32)^2}$$

$$\sigma=\sqrt{\frac18*\frac94+\frac38*\frac14+\frac38*\frac14+\frac18*\frac94}$$

$$\sigma=\sqrt{\frac{24}{32}}=\sqrt{\frac34}=\frac{\sqrt3}{2}$$

good Q +1

Kudos [?]: 451 [0], given: 0

Intern
Joined: 15 Jan 2008
Posts: 10

Kudos [?]: 2 [0], given: 0

Re: Three fair coins are labeled with a zero (0) on one side and [#permalink]

### Show Tags

17 Jan 2008, 15:54
Good approach. This is a tough question. How likely is to get this on the GMAT?
Q+1!!

maratikus wrote:
variance of binomial distribution is n*p*(1-p), n = 3, p = 1/2
variance = 3*1/2*(1-1/2)= 3/4

stdev = sqrt(variance) = sqrt(3)/2

After many trials sample standard deviation is close to theoretical standard deviation = sqrt(3)/2.

C is the answer.

Kudos [?]: 2 [0], given: 0

SVP
Joined: 29 Aug 2007
Posts: 2470

Kudos [?]: 867 [0], given: 19

Re: Three fair coins are labeled with a zero (0) on one side and [#permalink]

### Show Tags

20 Aug 2008, 09:31
walker wrote:
C

$$\sigma=\sqrt{\frac{\sum(x-x_a)^2}{n}}$$

where, $$x$$ - the sum of 3 numbers
$$x_a$$ - the average sum.

probabilities for $$x$$:
$$x=0:$$ $$p_0=\frac18;$$ $$x=1:$$ $$p_1=\frac38;$$ $$x=2:$$ $$p_2=\frac38;$$ $$x=3:$$ $$p_3=\frac18$$

$$x_a=\frac32$$

$$n \to \infty$$ (n=1000 is very large number)

we can write:

$$\sigma=\sqrt{\frac18*(0-\frac32)^2+\frac38*(1-\frac32)^2+\frac38*(2-\frac32)^2+\frac18*(3-\frac32)^2}$$

$$\sigma=\sqrt{\frac18*\frac94+\frac38*\frac14+\frac38*\frac14+\frac18*\frac94}$$

$$\sigma=\sqrt{\frac{24}{32}}=\sqrt{\frac34}=\frac{\sqrt3}{2}$$

good Q +1

In addition to what walker did:

no matter how many times the trail is performed, the expected value of SD doesnot remain the same.
Attachments

SD Calculation.xls [15 KiB]

_________________

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT

Kudos [?]: 867 [0], given: 19

SVP
Joined: 30 Apr 2008
Posts: 1863

Kudos [?]: 627 [0], given: 32

Location: Oklahoma City
Schools: Hard Knocks
Re: Three fair coins are labeled with a zero (0) on one side and [#permalink]

### Show Tags

20 Aug 2008, 12:55
Is this really a question that is likely to be on the GMAT? It seems safe to say this is a 700+ question.
_________________

------------------------------------
J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a.

GMAT Club Premium Membership - big benefits and savings

Kudos [?]: 627 [0], given: 32

Senior Manager
Joined: 07 Jan 2008
Posts: 398

Kudos [?]: 311 [0], given: 0

Re: Three fair coins are labeled with a zero (0) on one side and [#permalink]

### Show Tags

03 Sep 2008, 02:58
It's quite hard. However, I got the same solution as Walker mentioned.

Kudos [?]: 311 [0], given: 0

Senior Manager
Joined: 16 Jul 2008
Posts: 288

Kudos [?]: 16 [0], given: 4

Re: Three fair coins are labeled with a zero (0) on one side and [#permalink]

### Show Tags

03 Sep 2008, 06:22
I read somewhere that the GMAT does not expect you to know the standard deviation formula.
_________________

http://applicant.wordpress.com/

Kudos [?]: 16 [0], given: 4

SVP
Joined: 07 Nov 2007
Posts: 1790

Kudos [?]: 1101 [0], given: 5

Location: New York
Re: Three fair coins are labeled with a zero (0) on one side and [#permalink]

### Show Tags

03 Sep 2008, 07:06
Nerdboy wrote:
I read somewhere that the GMAT does not expect you to know the standard deviation formula.

I read the same in MGMAT math book.

I am not sure whether will get these kind of problems in real GMAT ..
If yes... then definitely it is 750+ quesiton.,

Good question!! Good discussion..
_________________

Smiling wins more friends than frowning

Kudos [?]: 1101 [0], given: 5

Intern
Joined: 03 Sep 2008
Posts: 4

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

Re: Three fair coins are labeled with a zero (0) on one side and [#permalink]

### Show Tags

04 Sep 2008, 11:16
Well it was a tough question..I wonder if GMAT asks such questions

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

Manager
Joined: 15 Jul 2008
Posts: 205

Kudos [?]: 74 [0], given: 0

Re: Three fair coins are labeled with a zero (0) on one side and [#permalink]

### Show Tags

04 Sep 2008, 15:31
Thanks walker... i had forgotten that x was the sum of numbers....

walker wrote:
bhushangiri wrote:
Walker, can you point out the flaw in my approach. I know from binomial dist parameters that my approach is wrong... but i have forgotten why this approach is worng.

I did not dig deep, but maybe you forgot that x is "the sum of the numbers" and E(x)=3C0*0*1/2^3+3C1*1*1/2^3+3C2*2*1/2^3+3C3*3*1/2^3=0+3/8+6/8+3/8=12/8=3/2
E(x^2)=3C0*0*1/2^3+3C1*1*1/2^3+3C2*4*1/2^3+3C3*9*1/2^3=0+3/8+12/8+9/8=24/8=3
var[x]=E[x^2] - (E[x])^2=3-(3/2)^2=3/4

SD = sqrt(var[x]) = $$\frac{sqrt{3}}{2}$$

Kudos [?]: 74 [0], given: 0

Manager
Status: Essaying
Joined: 27 May 2010
Posts: 143

Kudos [?]: 9 [0], given: 8

Location: Ghana
Concentration: Finance, Finance
Schools: Cambridge
GMAT 1: 690 Q47 V37
GPA: 3.9
WE: Accounting (Education)
Re: Three fair coins are labeled with a zero (0) on one side and [#permalink]

### Show Tags

28 Nov 2011, 09:16
I pray I never meet this question

Kudos [?]: 9 [0], given: 8

Non-Human User
Joined: 09 Sep 2013
Posts: 14902

Kudos [?]: 287 [0], given: 0

Re: Three fair coins are labeled with a zero (0) on one side and [#permalink]

### Show Tags

19 Sep 2013, 13:41
Hello from the GMAT Club BumpBot!

Thanks to another GMAT 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.
_________________

Kudos [?]: 287 [0], given: 0

Intern
Joined: 19 Oct 2013
Posts: 7

Kudos [?]: 6 [0], given: 29

Location: India
Concentration: Finance, Marketing
GMAT 1: 720 Q50 V37
WE: Analyst (Internet and New Media)
Three fair coins are labeled with a zero (0) on one side and [#permalink]

### Show Tags

30 Jul 2016, 21:55
Three fair coins are labeled with a zero (0) on one side and a one (1) on the other side. Jimmy flips all three
coins at once and computes the sum of the numbers displayed. He does this over 1000 times, writing down
the sums in a long list. What is the expected standard deviation of the sums on this list?

(A) 1/2
(B) 3/4
(C)$$\sqrt{3}$$/2
(D)$$\sqrt{5}$$/2
(E) 5/4

Last edited by Vyshak on 30 Jul 2016, 22:29, edited 1 time in total.
Topic Merged

Kudos [?]: 6 [0], given: 29

Director
Status: Tutor - BrushMyQuant
Joined: 05 Apr 2011
Posts: 613

Kudos [?]: 810 [0], given: 59

Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE: Information Technology (Computer Software)
Re: Three fair coins are labeled with a zero (0) on one side and [#permalink]

### Show Tags

12 May 2017, 10:11
Top Contributor
Bunuel: Isn't this out of scope for GMAT?
JCLEONES wrote:
Three fair coins are labeled with a zero (0) on one side and a one (1) on the other side. Jimmy flips all three coins at once and computes the sum of the numbers displayed. He does this over 1000 times, writing down the sums in a long list. What is the expected standard deviation of the sums on this list?
(A) 1/2
(B) 3/4
(C)$$\sqrt{3}$$/2
(D)$$\sqrt{5}$$/2
(E) 5/4

[Reveal] Spoiler:
I don't know how to solve this question. Please provide full explanation.

Thanks

_________________

Ankit

Check my Tutoring Site -> Brush My Quant

GMAT Quant Tutor
How to start GMAT preparations?
How to Improve Quant Score?
Gmatclub Topic Tags
Check out my GMAT debrief

How to Solve :
Statistics || Reflection of a line || Remainder Problems || Inequalities

Kudos [?]: 810 [0], given: 59

Senior Manager
Joined: 15 Jan 2017
Posts: 326

Kudos [?]: 3 [0], given: 753

Re: Three fair coins are labeled with a zero (0) on one side and [#permalink]

### Show Tags

29 Aug 2017, 07:47
How did these values come about, mentioned below? The rest is just formula * probability, so I am clear about it.
probabilities for xx:
x=0:x=0: p0=1/8;p0=1/8; x=1:x=1: p1=3/8;p1=3/8; x=2:x=2: p2=3/ 8;p2=3/8; x=3:x=3: p3=1/8 p3=1/8

xa=3/2

Kudos [?]: 3 [0], given: 753

Re: Three fair coins are labeled with a zero (0) on one side and   [#permalink] 29 Aug 2017, 07:47

Go to page    1   2    Next  [ 22 posts ]

Display posts from previous: Sort by

# Three fair coins are labeled with a zero (0) on one side and

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

 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®.