For a continuous uniform distribution, the probability density function $f(x)$ is constant over the interval $[a, b]$, where $a$ and $b$ are the minimum and maximum values. In this case:

• Minimum class length $a = 50.0$ minutes
• Maximum class length $b = 52.0$ minutes

The probability of an event in a continuous uniform distribution over an interval $[a, b]$ is given by: $P(X < x) = \frac{x - a}{b - a}$

Here, we are asked to find the probability that the class length is less than $50.5$ minutes.

1. Substitute the values into the formula: $P(X < 50.5) = \frac{50.5 - 50.0}{52.0 - 50.0}$

2. Simplify: $P(X < 50.5) = \frac{0.5}{2.0} = 0.25$

Answer:

The probability that the class length is less than 50.5 minutes is 0.25 or 25%.

Would you like further details or have any questions?

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1. How would the probability change if the class length interval was 48.0 to 52.0 minutes?
2. What is the probability of selecting a class longer than 51.0 minutes?
3. How does a continuous uniform distribution differ from a discrete uniform distribution?
4. How can this concept apply to real-world scheduling issues?
5. What if the problem asked for the probability of a class length exactly 51 minutes?

Tip: In continuous uniform distributions, probabilities of exact values (like $P(X = x)$) are always zero because the probability density function is spread over an interval.