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# A vending machine is designed to dispense 8 oz. of coffee

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Manager
Joined: 02 Jul 2007
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A vending machine is designed to dispense 8 oz. of coffee [#permalink]  31 Aug 2007, 17:01
A vending machine is designed to dispense 8 oz. of coffee intto a cup. After a test that recorded the number of oz. of coffee in each of 1,000 cups dispensed by the vending machine, the 12 listed amounts, in oz., were selected from the data. If the 1,000 recorded amounts have a mean of 8.1 oz. and a standard deviation of 0.3 oz., how many of the 12 listed amounted are within 1.5 standard deviations of the mean?

7.51 8.22 7.86 8.36
8.09 7.83 8.30 8.01
7.73 8.25 7.96 8.53
Director
Joined: 22 Aug 2007
Posts: 572
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Kudos [?]: 14 [0], given: 0

Re: Gmatprep; standard deviation [#permalink]  31 Aug 2007, 17:28
gnr646 wrote:
A vending machine is designed to dispense 8 oz. of coffee intto a cup. After a test that recorded the number of oz. of coffee in each of 1,000 cups dispensed by the vending machine, the 12 listed amounts, in oz., were selected from the data. If the 1,000 recorded amounts have a mean of 8.1 oz. and a standard deviation of 0.3 oz., how many of the 12 listed amounted are within 1.5 standard deviations of the mean?

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

Do they ask these questions on GMAT?
Manager
Joined: 02 Jul 2007
Posts: 112
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Kudos [?]: 2 [0], given: 0

Yah, I was floored. This one came in the first GMATprep I took a couple of weeks ago. Needless to say, I completely guessed and moved on. No way was I answering that in under 2 min. Anyone have good shortcuts for stats questions like this?
Manager
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Kudos [?]: 13 [0], given: 0

mean=8.1 SD=0.3 Therefore 1.5SD=0.45

Hence all values that fall under 8.1-0.45 to 8.1+0.45 is within 1.5 SD from the mean.

i.e we should look out for values between 7.65 and 8.55

There are 11 such values.
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Regards

Subhen

Director
Joined: 22 Aug 2007
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Kudos [?]: 14 [0], given: 0

subhen wrote:
mean=8.1 SD=0.3 Therefore 1.5SD=0.45

Hence all values that fall under 8.1-0.45 to 8.1+0.45 is within 1.5 SD from the mean.

i.e we should look out for values between 7.65 and 8.55

There are 11 such values.

Please, can you post the formula or formulas according to which you derived text in bold...

thanks
Director
Joined: 11 Jun 2007
Posts: 932
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IrinaOK wrote:
subhen wrote:
mean=8.1 SD=0.3 Therefore 1.5SD=0.45

Hence all values that fall under 8.1-0.45 to 8.1+0.45 is within 1.5 SD from the mean.

i.e we should look out for values between 7.65 and 8.55

There are 11 such values.

Please, can you post the formula or formulas according to which you derived text in bold...

thanks

the question states that the SD = 0.3, and asks how many of the 12 listed amounts are 1.5 within the SD, so it is SD * 1.5 = 0.3 * 1.5 = 0.45. There is no tricky formula involved. From there we find the values that would be within 0.45 from the mean/average of 8.1. This range as explained above is between 7.65 and 8.55 (+/- 0.45). Hence from the list, we see that there are 11 out of 12 amounts.
Director
Joined: 22 Aug 2007
Posts: 572
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Kudos [?]: 14 [0], given: 0

beckee529 wrote:
IrinaOK wrote:
subhen wrote:
mean=8.1 SD=0.3 Therefore 1.5SD=0.45

Hence all values that fall under 8.1-0.45 to 8.1+0.45 is within 1.5 SD from the mean.

i.e we should look out for values between 7.65 and 8.55

There are 11 such values.

Please, can you post the formula or formulas according to which you derived text in bold...

thanks

the question states that the SD = 0.3, and asks how many of the 12 listed amounts are 1.5 within the SD, so it is SD * 1.5 = 0.3 * 1.5 = 0.45. There is no tricky formula involved. From there we find the values that would be within 0.45 from the mean/average of 8.1. This range as explained above is between 7.65 and 8.55 (+/- 0.45). Hence from the list, we see that there are 11 out of 12 amounts.

got it,

actually, it is wording and redundant numbers that make it look complex...

Thank you for explanation!

Still wonder what OA is.

gnr646, can you please post it?
Manager
Joined: 02 Jul 2007
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sorry, OA is was 11. I did the same thing - got tripped up in the wording.
GMAT Club Legend
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Location: Singapore
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Mean is given -> 8.1
S.D is given -> 0.3

1.5S.D = +/- 0.45 from mean -> so we need values between 7.65 and 8.55. There are 11 such values.

Even if you missed it, you can work out a range and pick from the choices given. 1 S.D is about 64.8% of the number of values, which works out to ~8 values are within 1 S.D. 2S.D is about 95.4% of the number of values which works out to ~slight above 11 of the values are within 2S.D. So you should be picking an answer between 8-11. Tough luck if your choices are 8,9,10,11 though....
CEO
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Re: Gmatprep; standard deviation [#permalink]  02 Sep 2007, 22:20
gnr646 wrote:
A vending machine is designed to dispense 8 oz. of coffee intto a cup. After a test that recorded the number of oz. of coffee in each of 1,000 cups dispensed by the vending machine, the 12 listed amounts, in oz., were selected from the data. If the 1,000 recorded amounts have a mean of 8.1 oz. and a standard deviation of 0.3 oz., how many of the 12 listed amounted are within 1.5 standard deviations of the mean?

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

ughh this question lol. Its so easy, but b/c of time pressure on my GMATPrep, I got it wrong. Entered the wrong choice neway if u don't know SD well, its pretty easy to learn.

mean is 8.1 So just add 1.5(.03)=.45 to 8.1 and subtract .45 from 8.1. You get 7.65-8.55 So just find the numbers that fall inbetween these two numbers. Ans is 11.
Re: Gmatprep; standard deviation   [#permalink] 02 Sep 2007, 22:20
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