Question

Think about a density curve that consists of two line segments. The first goes from the point (0, 1) to the point (0.7, 1). The second goes from (0.7, 1) to (0.9, 2) in the xy-plane. What percent of observations fall between 0.7 and 0.9?

Answer 1

The percentage of observations between 0.7 and 0.9 is 30%.

Explanation:

Consider the diagram below.

The percent of observation that lie between 0.7 and 0.9 is same as the area under the line made by the points (0.7, 1) and (0.9, 2).

Area under the line made by (0.7, 1) and (0.9, 2) = Area of rectangle ABCD

+ Area of triangle ABE

`=(1*0.2)+((1)/(2)*1*0.2)\\=0.2+0.1\\=0.3`

The percentage of observations between 0.7 and 0.9 is = 0.30 × 100 = 30%.

Thus, the percentage of observations between 0.7 and 0.9 is 30%.