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This question deals with a continuous uniform distribution between 50.0 and 52.0 minutes, and we need to find the probability that the class length is more than 51.2 minutes.

### Solution
For a continuous uniform distribution \( X \) between \( a = 50.0 \) and \( b = 52.0 \), the probability density function \( f(x) \) is:
\[
f(x) = \frac{1}{b - a} = \frac{1}{52.0 - 50.0} = \frac{1}{2}
\]

To find \( P(X > 51.2) \), we calculate the area under the distribution curve from 51.2 to 52.0.

1. **Calculate the range for \( X > 51.2 \):**
   \[
   P(X > 51.2) = \frac{b - 51.2}{b - a} = \frac{52.0 - 51.2}{2} = \frac{0.8}{2} = 0.4
   \]

### Answer
The probability that the class length is more than 51.2 minutes is:
\[
P(X > 51.2) = 0.40
\]

Please let me know if you want further details or have any questions.

### Related Questions
1. What is the probability that the class length is less than 51.2 minutes?
2. How would the answer change if the distribution range was between 49.0 and 52.0 minutes?
3. What is the probability that the class length is exactly 51.2 minutes in a continuous uniform distribution?
4. How would you find the probability if the distribution was not uniform but normally distributed?
5. What is the mean and variance of a uniform distribution over the interval \( [50.0, 52.0] \)?

### Tip
In a continuous uniform distribution, the probability of any specific single point (like exactly 51.2 minutes) is always zero, as we are dealing with continuous data over an interval.

The lengths of a professor’s classes has a continuous uniform distribution between 50.0 min and 52.0 min. If one such class is randomly selected, find the probability that the class length is more than 51.2 min.

Learn how to calculate the probability that the length of a professor's class exceeds 51.2 minutes, given a continuous uniform distribution between 50.0 and 52.0 minutes. This problem explores the concepts of uniform distribution and probability, suitable for college-level students.

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