The standard deviation ({SD}) = 2;

3 standard deviations below the mean is greater than 43:

{Mean} - 3*{SD} > 43;
{Mean} - 6 > 43;
{Mean} > 49.

Answer: E.
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Hello Bunuel,
Could you mind explaining what "2 (or 3) deviation below/above mean' means? I could apply formula to solve such question but I don't really understand the nature of the problem?

Thank you indeed,

The standard deviation of a set is some number as well as the mean. We are told that 3 standard deviations below the mean is greater than 43. 3 standard deviations below the mean is {Mean} - 3*{SD}, which we are told that is greater than 43.

Hope that similar questions given here will help to understand better.
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Hi All,

Presenting the visual representation of the normal distribution curve:

A normal distribution curve is also known as the bell curve.




Such questions on standard deviation are centered around the following 4 variables:

I. Mean of the distribution
II. Standard Deviation of the distribution
III. A data point of the distribution
IV. Distance of data point from the mean

These variables are related as

Data Point = Mean +/- Distance from the mean where the distance from mean is expressed in terms of standard deviation

Out of these 4 variables, the question is likely to give you 3 and ask you to find the fourth variable.

Let's see what have we been given in the question statement

I. Mean- Need to find (let's assume it to be \(m\))
II. Standard deviation of the distribution - \(2\)
III. A data point of the distribution- \(43\)
IV. Distance of data point from the mean - \(3\) standard deviations below mean

We can write

\(43 < m - 3 * 2\) ( we put in a '-' sign as the data point is below mean)

\(m > 49\). Out of the given options only Option E has a value greater than \(49\).


Hope this helps

Regards
Harsh
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Aside: The topic of normal distributions is beyond the scope of the GMAT

Cheers,
Brent
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m-3sd>43

m-6>43 [As sd is 3 given]

m>49

The answer is 50 E,
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