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Coffee machine / SD

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by yass20015 » Fri Aug 07, 2015 1:08 pm
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. 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 SD of the mean? the tewelve listed: 7.51 / 8.22 / 7.86 etc... How we can resolve this ? what is the concept ? I don 't really understand the SD questions ? many thanks
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by Brent@GMATPrepNow » Fri Aug 07, 2015 1:17 pm
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
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by nikhilgmat31 » Tue Aug 11, 2015 10:31 pm
Great word problem. but simple to answer.

trick was to find new SD i.e. 1.5 * .3 = .45
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by anant03 » Mon Sep 14, 2015 8:37 am
Hi Experts ,

I don't understand the question and the solution, can you please give some other approach. I got this one wrong in my CAT.

Please advise.

Thanks in advance...
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by Brent@GMATPrepNow » Mon Sep 14, 2015 9:09 am
anant03 wrote:Hi Experts ,

I don't understand the question and the solution, can you please give some other approach. I got this one wrong in my CAT.

Please advise.

Thanks in advance...
try watching this free video on units of standard deviation and see if it helps: https://www.gmatprepnow.com/module/gmat- ... /video/809
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by [email protected] » Mon Sep 14, 2015 9:29 am
Hi anant03,

Here's a broader discussion on this question:

https://www.beatthegmat.com/gmat-prep-qu ... 77848.html

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by Amrabdelnaby » Wed Nov 18, 2015 4:59 am
I
I
I
I-----------------------------8.55
I
I-----------------------------8.1
I
I----------------------------- 7.65
I
I----------------------------- Zero


All what we need to do is to find the numbers between 8.55 and 7.65.

so the question asked us about how many numbers are within 1.5 SD from the mean.

we know that the mean is 8.1 and we know that the SD is 0.3

so 1.5 of SD is 1.5x 0.3 = 0.45

to find the numbers that are withing this standard deviation is to find all possible numbers that are dispersed from the mean by a maximum of 0.45, meaning that they could be max. away from the mean 0.45 either over the mean or under the mean.

to find numbers which are maximally above the mean by 0.45 , we add 8.1 to 0.45 and then find all the numbers within this range.

then to find the numbers which are maximally below the mean by 0.45 we subtract 0,45 from 8.1 to get 7.65 and look for all numbers within this range.

to simplify all of this, just draw the above figure with m in the middle, m+SD on the top and m-SD on the bottom and find all the numbers that lie within the range of M+SD and M-SD

BINGO!




yass20015 wrote: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. 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 SD of the mean? the tewelve listed: 7.51 / 8.22 / 7.86 etc... How we can resolve this ? what is the concept ? I don 't really understand the SD questions ? many thanks
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