https://file.aiquickdraw.com/mathbot/file/1729093116035swpjuv6e.jpg

The graph appears to depict a probability density function (PDF) of a continuous random variable, with a shaded region representing the probability of the variable falling within a specific interval. 

Looking at the shaded area on the graph, it seems to extend from \( x = 6 \) to \( x = 7 \), which means the probability represented by the shaded region is \( P(6 < x < 7) \).

Thus, the correct answer is:

**c. \( P(6 < x < 7) \)**

Would you like more details about how to interpret probability density functions or how this solution was reached?

Here are some questions for further exploration:
1. How is the total area under a probability density curve interpreted?
2. What is the difference between cumulative distribution function (CDF) and PDF?
3. How do we calculate the probability for continuous variables using definite integrals?
4. What would the graph look like for a different interval, like \( 7 < x < 10 \)?
5. How would this graph change if it represented a discrete probability distribution?

**Tip:** The area under a probability density function (PDF) over a given interval represents the probability that the random variable falls within that interval.

What does the shaded area represent? P(__ < x < __)

This problem involves identifying the probability represented by a shaded area under a probability density function (PDF) curve. The interval is determined based on the limits of the shaded area, here falling between 6 and 7. Key concepts include continuous random variables and the use of definite integrals to find probabilities.

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