Let's go through the questions in the images one by one, starting with the first one.

1. Question 1:

Which type of distribution does the graph illustrate?

The graph shows a rectangular or uniform distribution. A uniform distribution is one where all outcomes are equally likely within a specific range. In this case, the graph is flat between $x = 3$ and $x = 8$, meaning the probability is uniformly distributed over this interval.

2. Question 3:

Which type of distribution does the graph illustrate?

This is a normal distribution (also called a Gaussian distribution). The bell-shaped curve is symmetric around the mean (which in this case is $x = 0$). It is characterized by a peak at the mean and tails that decrease as you move away from the center.

3. Question 4:

What does the shaded area represent?

The shaded area under the curve between $x = 3$ and $x = 6$ represents the probability that a randomly selected value will fall between these two points. In terms of probability, this is written as $P(3 \leq x \leq 6)$.

4. Question 5:

What does the shaded area represent?

Similar to question 4, the shaded area represents the probability that the random variable $x$ lies between two specific values, say $x = 5$ and $x = 8$, denoted as $P(5 \leq x \leq 8)$. The curve looks like an exponential decay function.

5. Question 6:

For a continuous probability distribution, $0 \leq x \leq 15$, what is $P(x > 15)$?

For any probability distribution, the total probability is always 1. However, since $x$ cannot exceed 15 in this case (as the variable is constrained to $0 \leq x \leq 15$), the probability that $x > 15$ is 0.

Would you like more details on any of these? Let me know if you have any specific questions or want further clarification!

Here are some related questions to think about:

1. What is the formula for the probability density function (PDF) of a normal distribution?
2. How do you calculate the area under a uniform distribution?
3. What are the key properties that distinguish a normal distribution from an exponential distribution?
4. What is the cumulative distribution function (CDF) for a uniform distribution?
5. How do you find probabilities for continuous distributions when using integral calculus?

Tip: When working with probability distributions, always ensure that the area under the probability density curve sums up to 1 for valid distributions.