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Standard Deviation

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by arbiter » Sun Aug 23, 2009 7:37 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 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 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

OA is E
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Re: Standard Deviation

by ranell » Sun Aug 23, 2009 5:43 pm
arbiter 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. 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

OA is E

1.5 standard deviations of the mean equal 1,5*0,3 = 0,45. You simply need to calculate the number of 12 listed amounts are within 8,1-0,45=7,55 and 8,1+0,45=8,55 inclusive. You will have 11 figures
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by Thouraya » Wed May 11, 2011 12:17 am
It's 11 figures, so it's D (>10) not E (>11), no?

So it's all figures that are between 7.55 and 8.55?
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by Brent@GMATPrepNow » Wed May 11, 2011 2:39 pm
Thouraya wrote:It's 11 figures, so it's D (>10) not E (>11), no?
You're correct, Thouraya - the answer is 11. The original poster should have used brackets to show the answers as:
A) 4
B) 6
C) 9
D) 10
E) 11

I can see your confusion, when the answers appear to be inequalities :-)

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by Freakinout » Wed Aug 17, 2011 7:14 am
It should be between 8.1 - .45 = 7.65 (not 7.55 ) and 8.1 +0.45 = 8.65

Ans . 11
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by GmatKiss » Wed Aug 17, 2011 8:03 am
OA is D,10
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by MBA.Aspirant » Wed Aug 17, 2011 8:23 am
1.5 standard deviation = 0.45

values +/- 1.5 std = 7.56 < x < 8.55, 11 values fall within this range
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