Question

The area under the density curve that lies to the left of 10 is 0.654. What percentage of all possible observations of the variable are

a. less than 10

b. at least 10

Short answer

Percentage observations of the variable less than $10=65.4\%$, percentage observations of variable at least $10=34.6\%$

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 =$45.3$

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 under the density curve that lies to the left of $10=0.654$out of total area = $1$, so percentage of observations less than$10=65.4\%\hspace{0.17em}$

Hence, percentage of observations that are at least 10 includes observations that are greater than or equal to 10. These observations are to the right of $10$, so $1-0.654=34.6\%$