Question

Explain in your words why a density curve has two properties listed in Key Fact 6.1 on page 252

Short answer

Density curve depicts continuous outcomes probability. As probability > 0, so the curve lies on or above horizontal axis. As total probability = 1, so total area under the curve = 1

Step-by-step solution

Density Curve Meaning 

A Density Curve is a graphical representation of numerical distribution, having variable outcomes that are continuous.

Continuous Outcome variables can take non whole ie decimal values.

Like weight = $54.3$kgs , height = $5.4$foot

Properties 

The curve shows likelihood ( probability) of continuous variable' outcomes.

• A density curve is always on or above the horizontal axis - As probability of an outcome can never be negative, it is always equal to or more than $0$. So, the curve is always on or above horizontal axis
• The total area under a density curve (and above the horizontal axis) equals 1 - As total probability of all outcomes equals 1, so total area under the density curve also equal 1