GRE Quant reasoning

GRE Quant Problem Solving
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I am able to understand question correctly

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Concept - Suppose you have 2 sets of data. Your first set of data might have values ranging from 800 to 1000, with a mean of 920, and a standard deviation of 20. Your second set of data might have values ranging from 700 to 1100, with a mean of 910, and a standard deviation of 30. How will you compare the two datasets? or a particular entry (say 940) is deviant to what extent in both the datasets.
So what you do is,

  1. Bring the mean to the origin (0 on the number line or y-axis). i.e, subtract the mean from all the values of your dataset. Now, your data is spread about the origin on both sides (0 on the number line or y-axis). But your data is still dispersed differently.
  2. So you divide all the values of the dataset by standard deviation.

The value on the new graph to which your data corresponds is called the z score.
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So if a value of 920 is considered in the first dataset, then its z score will be 0 (since it is the mean)
Any value below the mean will have a negative z-score, and any above will have a positive one.

Now, in this data, if the entry is between +2 or -2 z-scores, you say, the entry is within 2 standard deviations about the mean.

Solution - You don’t need to solve for the z score every time.
If you want a number this is 2 standard deviations away, you can just add/subtract twice the value of standard deviation to/from the mean. In this case, 12 hours + (2x3 hours) = 18 hours and 12 hours - (2x3 hours) = 6 hours

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we need to calculate what is the range between 2 SD above or below the mean to determinate this problem. if mean is 12 then 2 SD below the mean is must be 12-2(3)=6 hours and 2 SD above the mean must be 12+2(3)=18 hours. so the range would be 6< study time <18 as they ask for within 2 SD of the mean of the distribution.
in that sense, the answer would be C, D, and E respectively.

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I finally understood I was calculating near points considering SD=2, but the question is asking that I have to go 2 SD (SD=3) right and left calculate the no and see which answer option falls in that range.

Thanks for your answers

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