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In a certain experiment, the data collected is the number of organisms

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In a certain experiment, the data collected is the number of organisms  [#permalink]

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New post 11 May 2015, 11:37
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In a certain experiment, the data collected is the number of organisms per sample, and this data follows a normal distribution. If the sample of data has a mean of 60 and a standard deviation of 12, which of the following is exactly 1.75 standard deviations more than the mean?

a) 48
b) 60
c) 72
d) 77.5
e) 81

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Re: In a certain experiment, the data collected is the number of organisms  [#permalink]

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New post 11 May 2015, 18:30
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Hi zxcvbnmas,

Standard Deviation is a relatively rare category in the Quant section, although you're like to be tested on it 1 time on Test Day. You'll never be asked to calculate SD though, so you really just need to learn the basic 'concepts' behind it.

Here, we're told two things about a group of numbers:
1) The average of the group is 60
2) The standard deviation of the group is 12

If you go 1 SD "up" from the average, you hit.....60+12 = 72
If you go 1 SD "down" from the average, you hit.....60-12 = 48

If you go 2 SDs "up" from the average, you hit.....60+2(12) = 84
If you go 2 SDs "down" from the average, you hit.....60-2(12) = 36
Etc.

Here, we're asked for the number that is EXACTLY 1.75 SDs above the mean....

1.75 SDs "up" would be.....60 + 1.75(12) = 81

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Re: In a certain experiment, the data collected is the number of organisms  [#permalink]

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New post 13 May 2015, 07:12
Please reference the somewhat crudely drawn normal curve. One standard deviation includes a range of values to the left and right of the mean. For a normal distribution, the majority of observation values will fall within a standard deviation of the mean. If one standard deviation is 12, then 1.75 standard deviations is 12 +3/4(12) = 21. We add and subtract 21 to and from the mean, 60.
60-21=39 (not an answer choice). 60+21=81 (Choice E)
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Re: In a certain experiment, the data collected is the number of organisms  [#permalink]

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New post 20 Apr 2018, 14:52
Top Contributor
zxcvbnmas wrote:
In a certain experiment, the data collected is the number of organisms per sample, and this data follows a normal distribution. If the sample of data has a mean of 60 and a standard deviation of 12, which of the following is exactly 1.75 standard deviations more than the mean?

a) 48
b) 60
c) 72
d) 77.5
e) 81


--------ASIDE--------------------------------------

A little extra background on standard deviations above and below the mean

If, for example, a set has a standard deviation of 4, then:
1 standard deviation = 4
2 standard deviations = 8
3 standard deviations = 12
1.5 standard deviations = 6
0.25 standard deviations = 1
etc

So, if the mean of a set is 9, and the standard deviation is 4, then:
2 standard deviations ABOVE the mean = 17 [since 9 + 2(4) = 17]
1.5 standard deviations BELOW the mean = 3 [since 9 - 1.5(4) = 3]
3 standard deviations ABOVE the mean = 21 [since 9 + 3(4) = 21]
etc.

----NOW ONTO THE QUESTION!!!!-----------------------------

1.75 standard deviations more than (aka ABOVE) the mean = 60 + (1.75)(12)
= 60 + 21
= 81
= E

Cheers,
Brent
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Re: In a certain experiment, the data collected is the number of organisms &nbs [#permalink] 20 Apr 2018, 14:52
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