The standard deviation of a normal distribution of data is 2

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