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Vending Machine Standard Deviation

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by RikaMueller » Sun Nov 28, 2010 2:20 am
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 1,000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data. If the 1,000 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 deviations of the mean?

5
6
9
10
11

Pls clarify.

Thanks a lot
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by Geva@EconomistGMAT » Sun Nov 28, 2010 3:18 am
1) std=0.3, so 1.5 standard deviations is 0.3*1.5 = 0.45.

2) "Within 1.5 stds from the mean" - could be higher or lower than the mean, as long as it's no more than 1.5 stds higher or 1.5 std lower from 8.1.
Thus, we want to count the number of terms that are in the range 8.1 +/- 0.45, or between 7.65 and 8.55

These are :

8.22
7.86
8.36
8.09
7.83
8.3
9.01
7.83
8.25
7.96
8.53

Basically, all but the first one 7.51: answer is 11.

[CORRECTED IN LATER POST]
Last edited by Geva@EconomistGMAT on Sun Nov 28, 2010 3:20 am, edited 1 time in total.
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by Geva@EconomistGMAT » Sun Nov 28, 2010 3:20 am
Geva@MasterGMAT wrote:1) std=0.3, so 1.5 standard deviations is 0.3*1.5 = 0.45.

2) "Within 1.5 stds from the mean" - could be higher or lower than the mean, as long as it's no more than 1.5 stds higher or 1.5 std lower from 8.1.
Thus, we want to count the number of terms that are in the range 8.1 +/- 0.45, or between 7.65 and 8.55

These are :

8.22
7.86
8.36
8.09
7.83
8.3
9.01
7.83
8.25
7.96
8.53

Basically, all but the first one 7.51: answer is 11.
Sorry, I missed 9.01, which is also outside the range. Answer is 10.
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by RikaMueller » Sun Nov 28, 2010 3:26 am
11 is right, because its 8.01 and not 9.01 :-)

Thanks so much, I didnt now how to approach this.
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by goyalsau » Sun Nov 28, 2010 7:13 am
the 1,000 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 deviations of the mean?
Geva@MasterGMAT wrote:
1) std=0.3, so 1.5 standard deviations is 0.3*1.5 = 0.45.
Thanks for the above explanation, I was not able to figure How to use 0.3 and 1.5
Thanks
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by Geva@EconomistGMAT » Sun Nov 28, 2010 8:01 am
goyalsau wrote:the 1,000 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 deviations of the mean?
Geva@MasterGMAT wrote:
1) std=0.3, so 1.5 standard deviations is 0.3*1.5 = 0.45.
Thanks for the above explanation, I was not able to figure How to use 0.3 and 1.5
Thanks
Many standard deviations questions don't actually require you to calculate std, or even know what it is. the question above belongs to a common variant of STD questions which simply uses the STD as a variable. You could replace STD with a generic variable x=0.3, and then ask how many of these numbers are in the range 8.1 +/- 1.5*x - the question would be the sam, and STD is just thrown in there for the "shock and awe" factor.
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by goyalsau » Sun Nov 28, 2010 8:17 am
Geva@MasterGMAT wrote:
goyalsau wrote:the 1,000 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 deviations of the mean?
Geva@MasterGMAT wrote:
1) std=0.3, so 1.5 standard deviations is 0.3*1.5 = 0.45.
Thanks for the above explanation, I was not able to figure How to use 0.3 and 1.5
Thanks
Many standard deviations questions don't actually require you to calculate std, or even know what it is. the question above belongs to a common variant of STD questions which simply uses the STD as a variable. You could replace STD with a generic variable x=0.3, and then ask how many of these numbers are in the range 8.1 +/- 1.5*x - the question would be the sam, and STD is just thrown in there for the "shock and awe" factor.

You are absolutely right, Because whenever i was the word STD I think No man i will not be able to solve it, But from now it will be better if I only consider as a range ,

What More disturbed me in this case is 1.5, I was not able to figure out Where to Use it, it is just a value that i have to multiply, Whenever I will see a STD problem i will definitely recall this statement of yours and will try to solve it from there on.
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by RikaMueller » Sun Nov 28, 2010 9:47 am
I had the same thought...how to use that 1.5 and 0.3. Now that I know how to solve this one, it seems so simple...thanks a ton :-)
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by Ankur87 » Fri Apr 12, 2013 3:28 am
hey Geva
Your answer : 11 is correct as it is 8.01 not 9.01
Answer : 11 out of 12 are within the range of 7.65 and 8.55.
Geva@MasterGMAT wrote:
Geva@MasterGMAT wrote:1) std=0.3, so 1.5 standard deviations is 0.3*1.5 = 0.45.

2) "Within 1.5 stds from the mean" - could be higher or lower than the mean, as long as it's no more than 1.5 stds higher or 1.5 std lower from 8.1.
Thus, we want to count the number of terms that are in the range 8.1 +/- 0.45, or between 7.65 and 8.55

These are :

8.22
7.86
8.36
8.09
7.83
8.3
9.01
7.83
8.25
7.96
8.53

Basically, all but the first one 7.51: answer is 11.
Sorry, I missed 9.01, which is also outside the range. Answer is 10.
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by rintoo22 » Sat Apr 13, 2013 4:09 am
Hi RikaMueller,

You must remember the defn of Standard deviation."SD indicates how far from the mean the data points typicall fall".
If you just pay attention to what the average dpread is doing you shoudl be fine.
It is unlikely that GMAT will ask you to calc the SD.
So change in SD 0.3 and mean 8.1 and rest you know already.
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by varun289 » Sat Apr 13, 2013 5:48 am
for better cal i can suggest to go with 810 - 765 range

1,5 stn dev mean = 1.5X st dv = 1.5*30 = 45

so ans=11

hope every one got that

easy problem yepp//
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by didieravoaka » Sat Nov 14, 2015 11:16 am
"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.

(From Bunuel Math expert -GMAT club)
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by Brent@GMATPrepNow » Sat Nov 14, 2015 11:52 am
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 ounces of coffee in each of thousands cup dispensed by vending machine ,the 12 listed amount in ounces ,were selected from data .if the 1000 recorded amount have a mean of 8.1 ounces and standard deviation of 0.3 ounce,how many of 12 listed amounts are within 1.5 standard deviation of the mean .

A. 4
B. 6
C. 9
D. 10
E. 11
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 [spoiler]11 (E)[/spoiler]

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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