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The problem describes a **uniform distribution** of airport security wait times between 0 and 10 minutes. The goal is to find the probability that a randomly selected person’s wait time is more than 7 minutes.

### Step-by-step solution:

1. **Uniform Distribution**:  
   The wait times are uniformly distributed between 0 and 10 minutes. For a uniform distribution, the probability density function (PDF) is constant within the given range (0 to 10).

2. **Range of interest**:  
   The event we are interested in is the wait time being more than 7 minutes. So, we need to find the probability that the wait time falls between 7 and 10 minutes.

3. **Total range of possible times**:  
   The total range of wait times is 0 to 10 minutes, so the length of the interval is 10 minutes.

4. **Interval for the event (more than 7 minutes)**:  
   The interval for wait times greater than 7 minutes is from 7 to 10 minutes. The length of this interval is:
   \[
   10 - 7 = 3 \, \text{minutes}
   \]

5. **Probability calculation**:  
   For a uniform distribution, the probability of an event occurring in a specific interval is the length of that interval divided by the total length of the distribution's range. So, the probability that a person waits more than 7 minutes is:
   \[
   P(X > 7) = \frac{3}{10} = 0.30
   \]

Thus, the probability that a randomly selected person’s wait time is more than 7 minutes is **0.30**.

### Do you want more details or have any questions?

Here are 5 related questions to expand on this concept:
1. What is the probability that a randomly selected person's wait time is less than 3 minutes?
2. How would the probability change if the distribution was not uniform?
3. Can you calculate the probability that the wait time is between 5 and 8 minutes?
4. What if the wait times were distributed uniformly between 0 and 15 minutes—how would the probability change?
5. How do uniform distributions differ from normal distributions in probability problems?

#### Tip:
For uniform distributions, probabilities are directly proportional to the length of the interval. This makes uniform distributions particularly straightforward to work with!

At a small regional airport, the wait times at airport security are evenly (uniformly) distributed between 0 and 10 minutes. Determine the probability that a randomly selected person's wait time is more than 7 minutes.

Learn how to calculate the probability that a person's wait time exceeds 7 minutes at a small regional airport where wait times are uniformly distributed between 0 and 10 minutes. The solution uses basic probability concepts, making it suitable for high school students.

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