Question

Given that $28.4\%$of all possible observations of the variable are less than $11$, determine the area under the density curve that lies to the

a. Left of $11$

b. Right of$11$

Short answer

Area under the density curve that lies to the left of $11=0.284$

Area under the density curve that lies to the right of$11=0.716$

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 = $45.3$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 $28.4\%$observations are less than $11$, so $28.4\%$of the total area $1=0.284$area of the density curve lies to the left of $11$.

Hence, remaining $71.6\%$of the observations are more than $11$, so $71.6\%$of the total area $1=0.716$area of the density curve lies to the right of $11$