Density Graphs Worksheet
Explore and interpret density graphs, understanding concepts like uniform, normal, and skewed distributions, and calculating probabilities.
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Standards
Topics
Density Graphs: Probability Distributions
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Read each question carefully and provide your answer in the space provided. For questions involving graphs, use the provided graph to answer.
1. What is the total area under any density curve?
2. Explain the difference between a density curve and a histogram.
Consider a continuous random variable X that is uniformly distributed between 0 and 10.
3. What is the height of the density curve for this uniform distribution?
4. Calculate the probability P(3 < X < 7). Show your work.
5. In a normal distribution, the mean, median, and mode are all located at the center of the curve.
True
False
6. A density curve with a long tail to the right is considered:
Symmetric
Left-skewed
Right-skewed
Uniform
7. The of a continuous random variable is a function whose graph is a density curve.
8. The rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean.
The graph below shows the density curve for a continuous random variable Y.
9. Calculate P(Y < 1).
Match each description with the correct type of density distribution.
1. Bell-shaped and symmetric
a. Uniform Distribution
2. All outcomes are equally likely
b. Normal Distribution
3. Data clustered at higher values with a tail to the left
c. Left-Skewed Distribution