The duration of a professor's class has a continuous uniform distribution between 50.0 minutes and 52.0 minutes. If one class is randomly selected, find the probability that the professor's duration of the class is more than 51 minutes. Round your answer to two decimal places.


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!

The duration of a professor's class has a continuous uniform distribution between 50.0 minutes and 52.0 minutes. If one class is randomly selected, find the probability that the professor's duration of the class is more than 51 minutes. Round your answer to two decimal places.

Find the probability that a professor's class lasts more than 51 minutes given a continuous uniform distribution between 50.0 and 52.0 minutes. This problem involves key concepts from probability theory, including uniform distribution and continuous random variables. Suitable for Grades 11-12.

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