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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, 10:37
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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, 17:30
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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, 06:12
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, 13:52
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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  [#permalink]

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New post 23 Oct 2019, 18:05
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


The value that is exactly 1.75 standard deviations more than the mean is:

60 + 1.75 x 12 = 60 + 21 = 81

Answer: E
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Re: In a certain experiment, the data collected is the number of organisms   [#permalink] 23 Oct 2019, 18:05

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

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