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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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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
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Re: Standard deviation of the mean? [#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


[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.

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

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New post 03 Nov 2010, 09:07
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.

Answer: E.[/quote]
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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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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New post 12 Nov 2012, 10:25
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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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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Collection of Questions:
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Re: Standard deviation of the mean? [#permalink]

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New post 17 Sep 2013, 03:37
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:
If the question had asked
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 provide your comments.
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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:
If the question had asked
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 provide your comments.


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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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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

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

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New post 18 Dec 2015, 05:09
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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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

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

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New post 22 Dec 2015, 03:32
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

Answer: Option E



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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New post 22 Dec 2015, 04:43
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

Answer: Option E



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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New post 23 Mar 2016, 08:52
Nice Question..
Here the questions want to know the number of values in the range mean + 1.5* S.D and mean -1.5*S.D
hence in the range (7.65 , 8.55)
Thus 11 values => E
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Re: A vending machine is designed to dispense 8 ounces of coffee [#permalink]

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New post 23 Jul 2016, 03:18
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


SD = 0.3 Ounce
therefore, 1.5 SD= 1.5* 0.3 = 0.45 Ounce

range of data 1.5 SD away from mean =from mean -1.5 SD to mean+1.5 SD

range of data 1.5 SD away from mean =from 8.1-0.45 to 8.1+0.45 = from 7.55 to 8.55

Out of the 12 data point given in the question the 11 data points data point falls in the range of 7.55 to 8.55 and 1 data point falls out of the range

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

THE CORRECT ANSWER IS E
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Re: A vending machine is designed to dispense 8 ounces of coffee [#permalink]

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New post 06 May 2017, 13:21
Why using 8.1 as the mean? How come the GMAT gives some useless information as "A vending machine is designed to dispense 8 ounces of coffee into a cup?" ;(

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New post 27 Jun 2017, 16:36
I would still like an explanation on the relationship between the .3 and the 1.5 since they are both SD. I would not have multiplied them, am I missing a law?

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

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New post 06 Jul 2017, 21:30
Quote:
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
8-7=1 and .55-.65=10 so 10+1=11

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

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New post 23 Jul 2017, 21:57
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


[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.

Answer: E.


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.

Please help

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

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New post 23 Jul 2017, 22:38
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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


[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.

Answer: E.


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.

Please help


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] 23 Jul 2017, 22:38

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