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The problem describes a situation where the wait times at airport security are uniformly distributed between 0 and 10 minutes. We need to determine the probability that a randomly selected person's wait time is less than 4.5 minutes.

### Step 1: Identify the key components
- The distribution is uniform between 0 and 10 minutes, meaning all wait times are equally likely.
- The random variable \( X \) represents the wait time and follows a **Uniform Distribution** \( U(0, 10) \).
- The probability density function (PDF) for a uniform distribution is:
  \[
  f(x) = \frac{1}{b - a} \quad \text{for} \quad a \leq x \leq b
  \]
  where \( a = 0 \) and \( b = 10 \).

### Step 2: Calculate the probability
We need to find \( P(X < 4.5) \). For a uniform distribution, this is simply the proportion of the interval \( [0, 10] \) that is less than 4.5:
\[
P(X < 4.5) = \frac{4.5 - 0}{10 - 0} = \frac{4.5}{10} = 0.45
\]

### Final Answer:
The probability that a randomly selected person's wait time is less than 4.5 minutes is **0.45**.

Would you like more details or have any questions?

### Related Questions:
1. What is the probability that a person's wait time is more than 7 minutes?
2. How do you calculate probabilities for other distributions like normal or exponential?
3. If the wait time range were extended to 20 minutes, how would the answer change?
4. How do you find the expected value for a uniform distribution?
5. What is the probability that the wait time is between 2 and 6 minutes?

### Tip:
In a uniform distribution, probabilities are calculated by comparing the lengths of intervals, making it easy to find probabilities for different ranges.

At a small regional airport, the wait times at airport security are uniformly distributed between 0 and 10 minutes. Determine the probability that a randomly selected person's wait time is less than 4.5 minutes.

Learn how to calculate the probability that a wait time at a small regional airport is less than 4.5 minutes. The problem involves uniform distribution between 0 and 10 minutes and applies key probability concepts. Suitable for high school students in Grades 11-12.

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