**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,

- 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.
- 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.

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**

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.

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