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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] New post 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] New post 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.

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

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] New post 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] New post 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 :-D
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Re: Standard deviation of the mean? [#permalink] New post 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] New post 12 Nov 2012, 09:37
Expert's post
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:
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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Re: Standard deviation of the mean? [#permalink] New post 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:
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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Re: Standard deviation of the mean? [#permalink] New post 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:
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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Re: A vending machine is designed to dispense 8 ounces of coffee [#permalink] New post 03 Nov 2014, 08:00
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A vending machine is designed to dispense 8 ounces of coffee [#permalink] New post 14 Jan 2015, 09:22
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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PS Standard Deviation question [#permalink] New post 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] New post 16 Mar 2015, 07:43
Expert's post
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.

Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules 1, 2, 3, and 7. Thank you.


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COLLECTION OF QUESTIONS:
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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Re: A vending machine is designed to dispense 8 ounces of coffee   [#permalink] 16 Mar 2015, 07:43
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