Question

Consider the density curve below. A density curve is plotted on an x y coordinate plane. The curve is a diagonal line segment which increases from (1, 0.25) to (3, 0.75). Find the probability that xxx is more than 222. P(x > 2)=P(x>2)=P, left parenthesis, x, is greater than, 2, right parenthesis, equals

Answer 1

To find the probability that x is greater than 2, we need to calculate the area under the density curve to the right of 2.

Step-by-step explanation:

To find the probability that x is greater than 2, we need to calculate the area under the density curve to the right of 2. The density curve is a diagonal line segment that increases from (1, 0.25) to (3, 0.75).

To calculate the probability, we need to find the area of the rectangle formed by the densities greater than 2.

First, let's find the area below the entire curve. The height of the curve at x = 2 is 0.5.

Therefore, the area under the entire curve is (2 - 1) * 0.5 = 0.5.

Next, let's find the area below the curve to the left of 2. The height of the curve at x = 2 is 0.5.

Therefore, the area below the curve and to the left of 2 is (2 - 1) * 0.5 = 0.5.

Finally, to find the probability that x > 2, we subtract the area to the left of 2 from the area under the entire curve. P(x > 2) = 0.5 - 0.5 = 0.