Standard Deviation

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arbiter: Senior | Next Rank: 100 Posts; Posts: 36; Joined: Mon Jun 09, 2008 9:17 am; Thanked: 2 times

by arbiter » Sun Aug 23, 2009 7:37 am

7.51 8.22 7.86 8.36
8.09 7.83 8.30 8.01
7.73 8.25 7.96 8.53

A vending machine is designed to dispense 8 ounces of coffee into a cup. After a test that recorded the number of ounces of coffee in each of 1000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data. If the 1000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.3 ounce, how many of the 12 listed amounts are within 1.5 standard deviations of the mean?

A> 4
B>6
C>9
D>10
E>11

OA is E

arbiter

Source: Beat The GMAT — Problem Solving | Sun Aug 23, 2009 7:37 am

ranell: Master | Next Rank: 500 Posts; Posts: 224; Joined: Mon May 04, 2009 2:44 pm; Location: Russia, Moscow; Thanked: 10 times; GMAT Score:730

Re: Standard Deviation

by ranell » Sun Aug 23, 2009 5:43 pm

arbiter wrote:7.51 8.22 7.86 8.36
8.09 7.83 8.30 8.01
7.73 8.25 7.96 8.53

A vending machine is designed to dispense 8 ounces of coffee into a cup. After a test that recorded the number of ounces of coffee in each of 1000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data. If the 1000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.3 ounce, how many of the 12 listed amounts are within 1.5 standard deviations of the mean?

A> 4
B>6
C>9
D>10
E>11

OA is E

1.5 standard deviations of the mean equal 1,5*0,3 = 0,45. You simply need to calculate the number of 12 listed amounts are within 8,1-0,45=7,55 and 8,1+0,45=8,55 inclusive. You will have 11 figures

Thouraya: Master | Next Rank: 500 Posts; Posts: 112; Joined: Wed Jan 20, 2010 5:46 am; Thanked: 1 times

by Thouraya » Wed May 11, 2011 12:17 am

It's 11 figures, so it's D (>10) not E (>11), no?

So it's all figures that are between 7.55 and 8.55?

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed May 11, 2011 2:39 pm

Thouraya wrote:It's 11 figures, so it's D (>10) not E (>11), no?

You're correct, Thouraya - the answer is 11. The original poster should have used brackets to show the answers as:
A) 4
B) 6
C) 9
D) 10
E) 11

I can see your confusion, when the answers appear to be inequalities

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Freakinout: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Mon Aug 01, 2011 8:09 pm; Location: India

by Freakinout » Wed Aug 17, 2011 7:14 am

It should be between 8.1 - .45 = 7.65 (not 7.55 ) and 8.1 +0.45 = 8.65

Ans . 11

GmatKiss: Legendary Member; Posts: 2789; Joined: Tue Jul 26, 2011 12:19 amFollowed by: 43 members; Location: Chennai, India; Thanked: 206 times; GMAT Score:640

by GmatKiss » Wed Aug 17, 2011 8:03 am

OA is D,10

MBA.Aspirant: Master | Next Rank: 500 Posts; Posts: 401; Joined: Tue May 24, 2011 1:14 amFollowed by: 5 members; Thanked: 37 times

by MBA.Aspirant » Wed Aug 17, 2011 8:23 am

1.5 standard deviation = 0.45

values +/- 1.5 std = 7.56 < x < 8.55, 11 values fall within this range

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