Question

Use the following information to answer questions 11 to 14.

A probability density curve is described by two line segments. The first connects the points (0,2) and (0.25,2). The second connects (0.25,2) to the x-axis.

Determine the x-value of the median of this curve.

Answer 1

The area under the curve from points (0,2) and (0.25,2) and x -axis = (0.25 - 0)*2 = 0.5

Now the area under the curve connecting point (0.25, 2) to the x-axis should be 1 - 0.5 = 0.5

Let it connect x-axis at point (a,0)

Thus, (a - 0.25)*2*1/2 = 0.5

-> a = 0.75

x value of median of the rectangular part of the curve = 0.125

x value of median of the triangular part of the curve

= 0.25 + (0.75 - 0.25)/3

= 5/12

Thus, the x-value of the median of this curve = 0.125*0.5 + 5/12*0.5

= 13/48 = 0.2708