Question
A density curve for all the possible ages between 0 years and 100 years is in the shape of a triangle. What is the height of the triangle?
Answers
GPT 3.5
The height of the triangle in a density curve represents the maximum density of the distribution. Since the total area under the density curve must equal 1 (since it represents the probability distribution), the area of the triangle should be 1.
The area of a triangle is given by the formula: Area = 0.5 * base * height.
Let's denote the base of the triangle (which represents the range of ages from 0 to 100 years) as 100 years. Since the area of the triangle is 1, we have:
1 = 0.5 * 100 * height
Solving for height, we get:
height = 1 / (0.5 * 100) = 1 / 50 = 0.02
Therefore, the height of the triangle in the density curve is 0.02.
The area of a triangle is given by the formula: Area = 0.5 * base * height.
Let's denote the base of the triangle (which represents the range of ages from 0 to 100 years) as 100 years. Since the area of the triangle is 1, we have:
1 = 0.5 * 100 * height
Solving for height, we get:
height = 1 / (0.5 * 100) = 1 / 50 = 0.02
Therefore, the height of the triangle in the density curve is 0.02.