The image you provided shows a question related to finding the probability of a certain event using a probability distribution graph.

Let me analyze the image and extract the mathematical content to provide a detailed solution.

Question Analysis: The question is asking for the probability that a randomly selected quantity is greater than 2. The graph shown seems to represent a probability distribution (likely a normal distribution or a similar continuous distribution).

To find the probability that a randomly selected quantity is greater than 2, we need to:

1. Determine the area under the curve to the right of 2 on the distribution graph.
2. This area represents the probability that the variable takes on a value greater than 2.

Solution Steps:

1. Identify the distribution: Based on the image, identify the type of distribution (e.g., normal distribution, uniform distribution, etc.).
2. Find the point of interest: Locate the value "2" on the x-axis.
3. Calculate the probability: The probability is the area under the curve to the right of this value.

Since I can't read the exact values or the specific details of the graph and answers due to the image's small size, I'll provide a generic method to solve such a problem:

General Method:

• For a Normal Distribution: You would typically use a Z-score table or a calculator to find the cumulative probability up to 2. Then, subtract this cumulative probability from 1 to get the probability that the variable is greater than 2.

  If $X \sim N(\mu, \sigma^2)$ is a normally distributed random variable:

  • Convert 2 into a Z-score: $Z = \frac{2 - \mu}{\sigma}$.
  • Use the Z-table to find $P(Z < z)$.
  • Compute $P(X > 2) = 1 - P(Z < z)$.

• For a Uniform Distribution: If the distribution is uniform, calculate the length of the interval from 2 to the maximum value and divide it by the total interval length.

Conclusion:

To provide a precise answer, I would need to know the specific type of distribution and the values involved. If you can provide more details or a clearer image, I can help you further with a more specific solution.

Would you like a detailed explanation of any specific type of distribution or more general questions about probability?

Related Questions:

1. How do you calculate probabilities for normal distributions?
2. What is the Z-score, and how is it used in probability calculations?
3. How do you interpret the area under a probability distribution curve?
4. What are cumulative probabilities, and why are they important?
5. How can you use technology, like calculators or software, to compute probabilities?

Tip: Understanding the type of distribution you are working with (normal, uniform, binomial, etc.) is crucial for calculating probabilities correctly. Make sure to familiarize yourself with different distributions and their properties.