Question

The area under the density curve that lies between $15$and $20$is $0.414$. What percentage of all possible observations of the variable are either less than $15$or greater than $20$?

Short answer

Percentage of the variable's observations less than $15$or greater than $20$= $58.6\%$

Step-by-step solution

Density Curve Concept 

Density Curve is a graphical representation of numerical distribution, having variable outcomes that are continuous (which can take non whole values), like weight = $54.3$Kgs

Density Curve Probability 

It shows likelihood ( probability) of continuous variable' outcomes. As total probability = $1$, total area under the curve is also equal to $1$.

Percentage of total observations that lie within a range is equal to percentage of area under the curve between the corresponding values.

Explanation

As total area = $1$& area between values $15$& $20$= $0.414$

So area to the left of $15$or to the right of $20$= total area - area between the numbers = $1-0.414=0.586$

Hence, percentage of observations less than $15$or greater than $20$=$58.6\%$