Standard Deviation

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Nidhs: Senior | Next Rank: 100 Posts; Posts: 69; Joined: Sun Jan 06, 2008 7:12 pmFollowed by: 1 member; Thanked: 3 times

by Nidhs » Fri Feb 08, 2008 5:53 pm

Brett discovers that 150 bags of his favorite cookie contain a total of 3750 cookies. He then determines that the cookies in a bag are normally distributed with a standard deviation of 5. When Brett goes to the store to buy a bag of his favorite cookies, how many of the 1200 bags in the store contain more than 30 cookies?

24

25

50

192

600

Does anyone know how to solve this??????

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Source: Beat The GMAT — Problem Solving | Fri Feb 08, 2008 5:53 pm

smushkas: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Sun Jul 01, 2007 5:56 pm; Thanked: 3 times

by smushkas » Sun Feb 10, 2008 4:39 am

Well, first of all, find the mean of 150 bags. 3750 / 150 = 25
Then we know it is a Normal Distribution that has:
1 SD = 68% of the total
2 SD = 95% of the total
3 SD = 99.7% of the total
Our data should be more than 30 cookies, that is more than 1 SD above. Thus, 1 - .68 = .32 = 32%
This 32% contains what is below the mean and what is above the mean, therefore we divide it by 2 to get what is above the mean, ==> .32 / 2 = .16 = 16%
.16 * 1200 = 192 ==> The answer must be [D]

What is the correct answer?

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Nidhs: Senior | Next Rank: 100 Posts; Posts: 69; Joined: Sun Jan 06, 2008 7:12 pmFollowed by: 1 member; Thanked: 3 times

by Nidhs » Tue Mar 04, 2008 5:08 pm

Can someone please explain to me how 1 SD is 68% of the total and so on

Thanks

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Tue Mar 04, 2008 8:05 pm

You shouldn't need to know that much detail about standard deviation for the GMAT.

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Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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resilient: Legendary Member; Posts: 789; Joined: Sun May 06, 2007 1:25 amFollowed by: 6 members; Location: Southern California, USA; Thanked: 15 times

sd

by resilient » Tue Mar 04, 2008 8:22 pm

with S.D. all you might want to look at is how they are dispersed. Litteraly knowing th ewebsters dictionary definition of the SD is all you might want to know.

Appetite for 700 and I scraped my plate!

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Nidhs: Senior | Next Rank: 100 Posts; Posts: 69; Joined: Sun Jan 06, 2008 7:12 pmFollowed by: 1 member; Thanked: 3 times

by Nidhs » Wed Mar 05, 2008 8:13 pm

I am relieved to know. I dont remember now where i got this question from....probably princeton or something.

Thanks.

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