Math Problem Statement
Solution
The question is asking about the shaded area under a continuous distribution curve. Based on the image, the shaded area appears to be between and on the horizontal axis.
To answer the question:
- The shaded area under the curve represents the probability that the variable lies within a certain range. Specifically, since the shaded area is between 6 and 7, this corresponds to the probability .
Thus, the correct answer is:
.
Would you like more details or have any other questions?
Here are 5 related questions that could help you further:
- How is the area under a probability density function related to probability?
- What are some common types of continuous distributions?
- How do you calculate probabilities for continuous distributions?
- How does the shape of the probability density function affect the probabilities?
- What is the significance of intervals in probability distributions?
Tip: For continuous distributions, the probability of a single point (e.g., ) is always zero because probability is represented by the area under the curve over an interval.
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Math Problem Analysis
Mathematical Concepts
Probability
Continuous Distribution
Area Under the Curve
Formulas
P(a < x < b) = ∫[a,b] f(x) dx
Theorems
Probability Density Function (PDF)
Suitable Grade Level
College Level (Statistics)
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