Given that the class duration follows a continuous uniform distribution between 50.0 minutes and 52.0 minutes, we are tasked with finding the probability that the class duration is more than 51 minutes.

Step 1: Uniform distribution formula

The probability density function (PDF) for a continuous uniform distribution is given by: $f(x) = \frac{1}{b - a} \quad \text{for} \quad a \leq x \leq b$ where $a$ and $b$ are the minimum and maximum values, respectively. In this case, $a = 50.0$ and $b = 52.0$.

Step 2: Determine the relevant interval

We are interested in the probability that the class duration $X$ is greater than 51 minutes. This can be expressed as: $P(X > 51) = \frac{\text{Length of interval for } X > 51}{\text{Length of total interval}}$

The total interval is from 50.0 to 52.0, so its length is: $b - a = 52.0 - 50.0 = 2.0 \, \text{minutes}$

The length of the interval for $X > 51$ is: $52.0 - 51.0 = 1.0 \, \text{minute}$

Step 3: Calculate the probability

Now, the probability can be computed as: $P(X > 51) = \frac{1.0}{2.0} = 0.5$

Thus, the probability that the professor's class duration is more than 51 minutes is $0.50$.

Final Answer:

The probability is 0.50 or 50%.

Would you like further details or clarification on this?

Here are some related questions:

1. How would you calculate the probability for a class duration between 51 and 51.5 minutes?
2. What if the class duration followed a normal distribution instead of a uniform distribution?
3. How would the probability change if the class duration had a range from 49.5 to 52.5 minutes?
4. What is the expected value of a uniformly distributed random variable between 50.0 and 52.0 minutes?
5. How does the uniform distribution differ from other continuous distributions, like exponential or normal distributions?

Tip: For uniform distributions, probabilities are proportional to the length of the interval you're interested in!