A vending machine is designed to dispense 8 ounces of coffee : GMAT Problem Solving (PS)
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# A vending machine is designed to dispense 8 ounces of coffee

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A vending machine is designed to dispense 8 ounces of coffee [#permalink]

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27 Apr 2010, 05:21
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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 above. If the 1000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.3 ounces, how many of the 12 listed amounts are within 1.5 standard deviation of the mean?

A. Four
B. Six
C. Nine
D. Ten
E. Eleven
[Reveal] Spoiler: OA
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Re: Standard deviation of the mean? [#permalink]

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27 Apr 2010, 07:26
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zz0vlb 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 above. If the 1000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.3 ounces, how many of the 12 listed amounts are within 1.5 standard deviation of the mean?

A. four
b. Six
c. Nine
d. Ten
e. Eleven

[Reveal] Spoiler:
e

Source: GMAT Prep

"Within 1.5 standard deviation of the mean" - means in the range {mean-1.5*sd; mean+1.5*sd} = {8.1-1.5*0.3; 8.1+1.5*0.3} = {7.65; 8.55}.

From the 12 listed amounts, only one (7.51) is out of this range and 11 are within this range.

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Re: Standard deviation of the mean? [#permalink]

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27 Apr 2010, 08:43
got it bunuel. thanks. Your explanation is very clear.
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Re: Standard deviation of the mean? [#permalink]

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03 Nov 2010, 08:07
Source: GMAT Prep[/quote]

"Within 1.5 standard deviation of the mean" - means in the range {mean-1.5*sd; mean+1.5*sd} = {8.1-1.5*0.3; 8.1+1.5*0.3} = {7.65; 8.55}.

From the 12 listed amounts, only one (7.51) is out of this range and 11 are within this range.

hi Bunuel,
I have not get clear why you take: 1.5*0.3
did i miss something? Please explain for me
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Re: Standard deviation of the mean? [#permalink]

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03 Nov 2010, 08:19
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MICKEYXITIN wrote:
hi Bunuel,
I have not get clear why you take: 1.5*0.3
did i miss something? Please explain for me

We are given that SD=0.3 and mean=8.1. Question: how many of the 12 listed amounts are within 1.5 standard deviation of the mean?

1.5 standard deviation equals to 1.5*SD=1.5*0.3=0.45, so "within 1.5 standard deviation of them mean" - means in the range {8.1-0.45; 8.1+0.45} = {7.65; 8.55}.

Hope it's clear.
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Re: Standard deviation of the mean? [#permalink]

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03 Nov 2010, 09:23
Bunuel wrote:
MICKEYXITIN wrote:
hi Bunuel,
I have not get clear why you take: 1.5*0.3
did i miss something? Please explain for me

We are given that SD=0.3 and mean=8.1. Question: how many of the 12 listed amounts are within 1.5 standard deviation of the mean?

1.5 standard deviation equals to 1.5*SD=1.5*0.3=0.45, so "within 1.5 standard deviation of them mean" - means in the range {8.1-0.45; 8.1+0.45} = {7.65; 8.55}.

Hope it's clear.

yes thanks Bunuel, i got it clear
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Re: Standard deviation of the mean? [#permalink]

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12 Nov 2012, 09:25
Bunuel wrote:
MICKEYXITIN wrote:
hi Bunuel,
I have not get clear why you take: 1.5*0.3
did i miss something? Please explain for me

We are given that SD=0.3 and mean=8.1. Question: how many of the 12 listed amounts are within 1.5 standard deviation of the mean?

1.5 standard deviation equals to 1.5*SD=1.5*0.3=0.45, so "within 1.5 standard deviation of them mean" - means in the range {8.1-0.45; 8.1+0.45} = {7.65; 8.55}.

Hope it's clear.

Does the range include specifically numbers 7.65 and 8.55?
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Re: Standard deviation of the mean? [#permalink]

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12 Nov 2012, 09:37
NON wrote:
Bunuel wrote:
MICKEYXITIN wrote:
hi Bunuel,
I have not get clear why you take: 1.5*0.3
did i miss something? Please explain for me

We are given that SD=0.3 and mean=8.1. Question: how many of the 12 listed amounts are within 1.5 standard deviation of the mean?

1.5 standard deviation equals to 1.5*SD=1.5*0.3=0.45, so "within 1.5 standard deviation of them mean" - means in the range {8.1-0.45; 8.1+0.45} = {7.65; 8.55}.

Hope it's clear.

Does the range include specifically numbers 7.65 and 8.55?

Luckily we don't need to worry about it for this question, though I'd say yes, the range has to be inclusive.
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Re: Standard deviation of the mean? [#permalink]

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17 Sep 2013, 02:37
Bunuel wrote:
MICKEYXITIN wrote:
hi Bunuel,
I have not get clear why you take: 1.5*0.3
did i miss something? Please explain for me

We are given that SD=0.3 and mean=8.1. Question: how many of the 12 listed amounts are within 1.5 standard deviation of the mean?

1.5 standard deviation equals to 1.5*SD=1.5*0.3=0.45, so "within 1.5 standard deviation of them mean" - means in the range {8.1-0.45; 8.1+0.45} = {7.65; 8.55}.

Hope it's clear.

Hello Bunuel,
Would you please clear one doubt.
The question states that "how many of the 12 listed amounts are within1.5 standard deviation of the mean? In this case, do we need to consider boundary values as well such as (7.65) and (8.55).
I mean, If the question had 7.65 value, then would we have considered 7.65 value ? i.e 7.65<= std deviation <= 8.55 is the range
Another doubt:
Question: how many of the 12 listed amounts are between 1.5 standard deviation of the mean?, and the answer choice had 7.65 as the value

Then, do we need to consider 7.65 value while answering ? I believe, not and 7.65< std deviation < 8.55 will be the range
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Re: Standard deviation of the mean? [#permalink]

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17 Sep 2013, 02:41
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imhimanshu wrote:
Bunuel wrote:
MICKEYXITIN wrote:
hi Bunuel,
I have not get clear why you take: 1.5*0.3
did i miss something? Please explain for me

We are given that SD=0.3 and mean=8.1. Question: how many of the 12 listed amounts are within 1.5 standard deviation of the mean?

1.5 standard deviation equals to 1.5*SD=1.5*0.3=0.45, so "within 1.5 standard deviation of them mean" - means in the range {8.1-0.45; 8.1+0.45} = {7.65; 8.55}.

Hope it's clear.

Hello Bunuel,
Would you please clear one doubt.
The question states that "how many of the 12 listed amounts are within1.5 standard deviation of the mean? In this case, do we need to consider boundary values as well such as (7.65) and (8.55).
I mean, If the question had 7.65 value, then would we have considered 7.65 value ? i.e 7.65<= std deviation <= 8.55 is the range
Another doubt:
Question: how many of the 12 listed amounts are between 1.5 standard deviation of the mean?, and the answer choice had 7.65 as the value

Then, do we need to consider 7.65 value while answering ? I believe, not and 7.65< std deviation < 8.55 will be the range

Please check the post just above yours: a-vending-machine-is-designed-to-dispense-8-ounces-of-coffee-93351.html#p1142674

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Re: A vending machine is designed to dispense 8 ounces of coffee [#permalink]

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A vending machine is designed to dispense 8 ounces of coffee [#permalink]

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14 Jan 2015, 09:22
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So:
M= 8.1
SD= 0.3
1.5 SD= 1 SD plus 1/2 SD, which is 0.3+0.15=0.45 SD.

Lets add and subtract 3SD or 0.45 from the M or 8.1:
8.1 - 0.45 = 7.65
8.1 + 0.45 = 8.55

So, we are looking for numbers in this range 7.65<numbers<8.55.

These are 11 of the 12 numbers, ANS E.
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16 Mar 2015, 07:33
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 deisgned to dispense 8 ounces of coffee into a cup. After a test that recorded the number of ounces of coffee in each of 1000cups 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 (CORRECT)

11 is the correct answer, but why?
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Re: A vending machine is designed to dispense 8 ounces of coffee [#permalink]

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16 Mar 2015, 07:43
Jeli13 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 deisgned to dispense 8 ounces of coffee into a cup. After a test that recorded the number of ounces of coffee in each of 1000cups 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 (CORRECT)

11 is the correct answer, but why?

Merging topics.

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A vending machine is designed to dispense 8 ounces of coffee [#permalink]

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18 Dec 2015, 04:09
I understand that this is an old post. But all the explanations above dont make sense to me. none really makes sense to me. The standard deviation question is one i havent got a good grip of. i solicit the help of experts like @veritasprep or if I'm lucky, GMATPrepNow
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Re: A vending machine is designed to dispense 8 ounces of coffee [#permalink]

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22 Dec 2015, 00:18
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zz0vlb 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 above. If the 1000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.3 ounces, how many of the 12 listed amounts are within 1.5 standard deviation of the mean?

A. Four
B. Six
C. Nine
D. Ten
E. Eleven

Mean = 8.1
Standard Deviation = 0.3

within 1.5 standard deviation of the mean

i.e. 1.5 standard deviation ABOVE the mean = 8.1+1.5*0.3 = 8.55
and 1.5 standard deviation BELOW the mean = 8.1-1.5*0.3 = 7.65

Except first value 7.51, all other values are within the range hence, 11 values fall within 1.5 SD from Mean

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Re: A vending machine is designed to dispense 8 ounces of coffee [#permalink]

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22 Dec 2015, 02:32
GMATinsight wrote:
zz0vlb 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 above. If the 1000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.3 ounces, how many of the 12 listed amounts are within 1.5 standard deviation of the mean?

A. Four
B. Six
C. Nine
D. Ten
E. Eleven

Mean = 8.1
Standard Deviation = 0.3

within 1.5 standard deviation of the mean

i.e. 1.5 standard deviation ABOVE the mean = 8.1+1.5*0.3 = 8.55
and 1.5 standard deviation BELOW the mean = 8.1-1.5*0.3 = 7.65

Except first value 7.51, all other values are within the range hence, 11 values fall within 1.5 SD from Mean

Thanks GMATinsight but why did you have multiply 1.5 with 0.3?
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Re: A vending machine is designed to dispense 8 ounces of coffee [#permalink]

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22 Dec 2015, 03:43
Nez wrote:
GMATinsight wrote:
zz0vlb 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 above. If the 1000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.3 ounces, how many of the 12 listed amounts are within 1.5 standard deviation of the mean?

A. Four
B. Six
C. Nine
D. Ten
E. Eleven

Mean = 8.1
Standard Deviation = 0.3

within 1.5 standard deviation of the mean

i.e. 1.5 standard deviation ABOVE the mean = 8.1+1.5*0.3 = 8.55
and 1.5 standard deviation BELOW the mean = 8.1-1.5*0.3 = 7.65

Except first value 7.51, all other values are within the range hence, 11 values fall within 1.5 SD from Mean

Thanks GMATinsight but why did you have multiply 1.5 with 0.3?

1.5 standard deviation means 1.5*Standard Deviation

i.e. 1.5 standard deviation ABOVE the mean = 8.1+1.5*0.3 = 8.55
and 1.5 standard deviation BELOW the mean = 8.1-1.5*0.3 = 7.65

I hope this helps!
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A vending machine is designed to dispense 8 ounces of coffee [#permalink]

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25 Dec 2015, 09:24
Thanks GMATinsight.
You had good intentions, but that DID NOT HELP.
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Re: A vending machine is designed to dispense 8 ounces of coffee [#permalink]

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16 Mar 2016, 15:35
Nez wrote:
Thanks GMATinsight.
You had good intentions, but that DID NOT HELP.

I know you asked this question a while ago but what did you not understand? I would like to help you . Hope to hear from you soon.
Re: A vending machine is designed to dispense 8 ounces of coffee   [#permalink] 16 Mar 2016, 15:35

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