Question

what would the height need to be for this curve to be a density curve?
-\frac{1}{6}
\frac{1}{6}
\frac{1}{5}
1

Explanation:

Step1: Recall the property of a density curve

The area under a density curve is \(1\). For a rectangular density curve, the area \(A = \text{base}\times\text{height}\).

Step2: Calculate the base length

The base length \(b\) of the rectangle is \(1-(- 5)=6\). Let the height be \(h\). Using the formula \(A = b\times h\), and since \(A = 1\), we have \(1=6\times h\).

Step3: Solve for \(h\)

From \(1 = 6h\), we can solve for \(h\) by dividing both sides of the equation by \(6\). So \(h=\frac{1}{6}\).

Answer:

\(\frac{1}{6}\) (the second option)