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GMAT Prep question

by anksm22 » Sun Jul 20, 2014 1:39 am

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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 no of ounces of coffee in each of 1000 cups dispenced by th vending machine, the 12 listed amount, in ouncec, were selected from the data. If the 1000 recorded amounts havea mean of ounces and a 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


Please explain the question and how to do it.
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by Brent@GMATPrepNow » Sun Jul 20, 2014 2:24 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]

For more info on this concept, see the following video: https://www.gmatprepnow.com/module/gmat ... /video/809

Cheers,
Brent
Last edited by Brent@GMATPrepNow on Fri Jun 24, 2016 9:48 am, edited 1 time in total.
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by GMATGuruNY » Sun Jul 20, 2014 2:24 am
The problem as posted is missing necessary information.
It should read as follows:
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
1.5 standard deviations BELOW the mean = mean - (1.5)(standard deviation) = 8.1 - (1.5)(.3) = 7.65.
1.5 standard deviations ABOVE the mean = mean + (1.5)(standard deviation) = 8.1 + (1.5)(.3) = 8.55.
Any value between 7.65 and 8.55 is within 1.5 standard deviations of the mean.
Of the 12 values, only one value -- 7.51 -- is NOT between 7.65 and 8.55.
Thus, the remaining 11 values ARE within 1.5 standard deviations of the mean.

The correct answer is E.
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by anksm22 » Sun Jul 20, 2014 2:39 am
thank you. I got it
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by GMATinsight » Sun Jul 20, 2014 2:41 am
anksm22 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" refers to

within (Mean + 1.5 x Standard Deviation) and (Mean - 1.5 x Standard Deviation)

i.e. within (8.1 + 1.5 x 0.3) and (8.1 - 1.5 x 0.3)
i.e. within (8.1 + 0.45) and (8.1 - 0.45)
i.e. within (8.55) and (7.65)

The Highlighted amounts out of all listed amounts fall within the desired 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

i.e. Eleven amounts

Answer: option E
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by Jeff@TargetTestPrep » Thu Aug 30, 2018 4:49 pm
anksm22 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 no of ounces of coffee in each of 1000 cups dispenced by th vending machine, the 12 listed amount, in ouncec, were selected from the data. If the 1000 recorded amounts havea mean of ounces and a 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
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.

Answer: E

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