We are given a continuous uniform distribution for the duration of a professor's class, which is uniformly distributed between 50.0 minutes and 52.0 minutes. We are tasked with finding the probability that a randomly selected class will last more than 51.3 minutes.

Step 1: Understanding the uniform distribution

For a continuous uniform distribution, the probability density function (PDF) is constant over the interval $[a, b]$, where $a = 50.0$ and $b = 52.0$. The formula for the PDF of a uniform distribution is:

$f(x) = \frac{1}{b - a}, \text{ for } a \leq x \leq b$

In this case: $f(x) = \frac{1}{52.0 - 50.0} = \frac{1}{2.0} = 0.5$

Step 2: Calculate the required probability

We want the probability that the class duration exceeds 51.3 minutes. This can be expressed as:

$P(X > 51.3)$

For a uniform distribution, the probability is simply the proportion of the interval $[51.3, 52.0]$ relative to the total interval $[50.0, 52.0]$. This is given by the formula:

$P(X > 51.3) = \frac{b - 51.3}{b - a} = \frac{52.0 - 51.3}{52.0 - 50.0} = \frac{0.7}{2.0} = 0.35$

Step 3: Conclusion

Thus, the probability that the class duration is more than 51.3 minutes is:

$P(X > 51.3) = 0.35$

So, the answer is 0.35.

Would you like more details or have any questions?

Here are 5 related questions to explore further:

1. How do you find the mean of a continuous uniform distribution?
2. What is the probability that the class duration is less than 51 minutes?
3. How do you calculate the variance of a uniform distribution?
4. What would be the probability if the class duration was uniformly distributed between 45 and 55 minutes?
5. How would the problem change if the distribution were not uniform?

Tip: In a uniform distribution, the probability of an event is proportional to the length of the interval over which the event occurs.