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# A vending machine is designed to dispense 8 ouces of coffee

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Senior Manager
Joined: 13 Sep 2006
Posts: 264
Location: New York
A vending machine is designed to dispense 8 ouces of coffee  [#permalink]

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27 Nov 2006, 18:13
A vending machine is designed to dispense 8 ouces of coffee into a cup. After a test that recorded the number of ounces in a cup of coffee in each of 1,000 cups dispensed by the vending machine, the 12 listed amounts in ounces, (see below) were selected from the data. If the 1,000 recorded amounts have a mean of 8.1 and a standard deviation of .3 ounce, how many of the 12 listed amounts are within 1.5 standard deviations of the mean?

7.51 8.22 7.86 8.3
8.09 7.83 7.96 8.36
7.73 8.25 8.01 8.53

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

Argh - I can't figure out what I am doing wrong...Shouldn't the standard deviation yied a range of 7.8 - 8.4 hence 2 amounts are outside the standard deviation?? Please help

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Senior Manager
Joined: 20 Feb 2006
Posts: 370

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27 Nov 2006, 19:02
E for me

Mean = 8.1
SD = 0.3

Range of values within 1.5 SDs of mean is given by 7.65-8.55

11 values fall within this range
Director
Joined: 06 Feb 2006
Posts: 882

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28 Nov 2006, 00:43
Yes E....

Simply multiply 1.5*0.3=0.45

So the lowest possible value can be: 8.1-0.45=7.65
The highers possible value: 8.1+0.45=8.55
Senior Manager
Joined: 13 Sep 2006
Posts: 264
Location: New York

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28 Nov 2006, 16:27
SimaQ wrote:
Yes E....

Simply multiply 1.5*0.3=0.45

So the lowest possible value can be: 8.1-0.45=7.65
The highers possible value: 8.1+0.45=8.55

Thanks SimaQ - That helps! E it is
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Retired Moderator
Joined: 18 Jul 2008
Posts: 897

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04 Jan 2009, 19:31
Why do we need to multiple 1.5 * .3?

SimaQ wrote:
Yes E....

Simply multiply 1.5*0.3=0.45

So the lowest possible value can be: 8.1-0.45=7.65
The highers possible value: 8.1+0.45=8.55
Manager
Joined: 12 Oct 2008
Posts: 99

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04 Jan 2009, 20:37
Why do we need to multiple 1.5 * .3?

SimaQ wrote:
Yes E....

Simply multiply 1.5*0.3=0.45

So the lowest possible value can be: 8.1-0.45=7.65
The highers possible value: 8.1+0.45=8.55

because you are being asked for "within 1.5 standard deviations of the mean". Standard deviation is 0.3, 1.5 standard deviations is 0.45.
Manager
Joined: 07 Jan 2008
Posts: 85
Re: GMAT Prep - Standard Deviation  [#permalink]

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05 Jan 2009, 05:09
The range is always
M + factor * SD
M - factor * SD

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If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Re: GMAT Prep - Standard Deviation &nbs [#permalink] 05 Jan 2009, 05:09
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# A vending machine is designed to dispense 8 ouces of coffee

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