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Manager  Joined: 27 Feb 2010
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A vending machine is designed to dispense 8 ounces of coffee  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 73% (02:04) correct 27% (02:12) wrong based on 867 sessions

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 59622
Re: Standard deviation of the mean?  [#permalink]

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28
21
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

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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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
Math Expert V
Joined: 02 Sep 2009
Posts: 59622
Re: Standard deviation of the mean?  [#permalink]

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4
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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1
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?
Math Expert V
Joined: 02 Sep 2009
Posts: 59622
Re: Standard deviation of the mean?  [#permalink]

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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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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
Math Expert V
Joined: 02 Sep 2009
Posts: 59622
Re: Standard deviation of the mean?  [#permalink]

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9
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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A vending machine is designed to dispense 8 ounces of coffee  [#permalink]

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3
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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Re: A vending machine is designed to dispense 8 ounces of coffee  [#permalink]

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1
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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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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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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Re: A vending machine is designed to dispense 8 ounces of coffee  [#permalink]

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Bunuel 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

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.

Hi Bunuel, I am still not clear on this problem.

since 8.1 is the mean, i also assume 0.3 is the SD on this mean.

and if the questions asks 1.5 SD of the mean, doesn't it translate to 0.75 (1.5/2) either side of 1.5.

Why do we multiply the 1st SD and the 2nd.

Math Expert V
Joined: 02 Sep 2009
Posts: 59622
Re: A vending machine is designed to dispense 8 ounces of coffee  [#permalink]

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shettytarun wrote:
Bunuel 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

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.

Hi Bunuel, I am still not clear on this problem.

since 8.1 is the mean, i also assume 0.3 is the SD on this mean.

and if the questions asks 1.5 SD of the mean, doesn't it translate to 0.75 (1.5/2) either side of 1.5.

Why do we multiply the 1st SD and the 2nd.

I tried to explain this here: https://gmatclub.com/forum/a-vending-ma ... ml#p812247

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

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Top Contributor
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

If the Standard Deviation is 0.3 ounces, then 0.3 ounces represents 1 unit of standard deviation.
Similarly, 0.6 ounces represents 2 units of standard deviation,
0.15 ounces represents 0.5 units of standard deviation, and so on.

If the mean is 8.1 ounces, then we say that 8.4 ounces is 1 unit of standard deviation above the mean (since 8.1 + 0.3 = 8.4), and we say that 7.8 ounces is 1 unit of standard deviation below the mean (since 8.1 - 0.3 = 7.8)

We want to know how many measurements in the list are within 1.5 standard deviations of the mean

Well, using the above logic, 0.45 represents 1.5 units of standard deviation.

So, 1.5 units of standard deviation below the mean equals 7.65 (8.1 - 0.45 = 7.65)
Similarly, 1.5 units of standard deviation abovethe mean equals 8.55 (8.1 + 0.45 = 8.55)

So, any measurement that is between 7.65 ounces and 8.55 will be within 1.5 standard deviations of the mean.

In the given list of measurements, the following meet this requirement:

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

So the answer is 11 (E)

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

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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

We are given 12 listed amounts of coffee that we can put in order from least to greatest.

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

We need to determine how many of the listed amounts are within 1.5 standard deviations of the mean. Since the standard deviation is 0.3, 1.5 standard deviations is: 1.5 x 0.3 = 0.45.

1.5 standard deviations above the mean is 8.1 + 0.45 = 8.55

1.5 standard deviations below the mean is 8.1 – 0.45 = 7.65

We see that all the values are between 7.65 and 8.55 except 7.51. Thus, 11 values are within 1.5 standard deviation of the mean.

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