The image shows examples of right-skewed probability density curves. It gives three examples, where areas under the curve represent different probabilities. The image mentions examples such as 25% area to the right of c, 75% area to the left of c, and 30% area between a and b.

1. Problem Description

The image shows examples of right-skewed probability density curves. It gives three examples, where areas under the curve represent different probabilities. The image mentions examples such as 25% area to the right of c, 75% area to the left of c, and 30% area between a and b.

2. Solution Steps

The question doesn't require calculations, but rather explains the meaning of the probability density curves and the areas under them.

The probability density curve represents the distribution of a continuous random variable $X$. The area under the curve between any two points $x_1$ and $x_2$ (where $x_1 < x_2$) represents the probability that the random variable $X$ falls between $x_1$ and $x_2$. Mathematically, this is written as:

$P(x_1 \le X \le x_2) = \int_{x_1}^{x_2} f(x) dx$

where $f(x)$ is the probability density function.

For a right-skewed distribution, the tail on the right-hand side is longer than the tail on the left-hand side, meaning the distribution has more extreme values on the right.

The example in the image describes that:

* 25% area to the right of c means $P(X > c) = 0.25$

* 75% area to the left of c means $P(X < c) = 0.75$

* 30% area between a and b means $P(a < X < b) = 0.30$

3. Final Answer

The image illustrates right-skewed probability density curves and how the area under these curves represents the probability of a random variable falling within a certain range.