Question

Think about a density curve that consists of two line segments. The first goes from the point (0, 1) to the point (0.4, 1). The second goes from (0.4, 1) to (0.8, 2) in the xy-plane. What percent of observations fall below 0.40?a) .60b) 0.30c) 0.40d) 0.20e) 1.00

Answer 1

The diagram of the density curve is the image below(The first image uploaded)

The probability that observations (X) falls below 0.40 is the area under the curve for X < 0.40.

P 1 = 0.40 × 1 = 0.40

So, option d is correct.

Explanation:

To understand the answer above we need to know what a density curve is

A density curve is a graph that shows probability. The area under the density curve is equal to 100 percent of all probabilities. As we usually use decimals in probabilities you can also say that the area is equal to 1 (because 100% as a decimal is 1).

Now from our diagram we can say that the area under the graph is equal to 1 and we are told to find the percent of the observation that fall below 0.40 what this means is that we should find the percentage of the observation that fall within 0.40 of 1 which is the total area

P(Observation) = 0.40 × 1 = 0.40 for Observation < 0.40

Note to draw this graph we considered the points given in the question

X1 =0 , Y1 = 1

X2 = 0.4 , Y2 = 1

X3 = 0.4 , Y3 = 1

X4 = 0.8 , Y4 = 2