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 - shaped density curve (uniform distribution), the area formula is \(A=\text{base}\times\text{height}\).

Step2: Calculate the base length

The base of the rectangle (from \(x = - 5\) to \(x = 1\)) has length \(b=1-(-5)=6\).

Step3: Solve for the height

Let the height be \(h\). Using the formula \(A = b\times h\) and since \(A = 1\), we substitute \(b = 6\) into \(1=6\times h\). Then \(h=\frac{1}{6}\).

Answer:

\(\frac{1}{6}\)