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 asData 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