Given that the completion times are uniformly distributed between 9.8 minutes and 18.4 minutes, we can use the formula for the probability of an interval under a uniform distribution:

$P(a \leq X \leq b) = \frac{b - a}{\text{max} - \text{min}}$

Where:

• $a = 13.5$
• $b = 17.5$
• $\text{max} = 18.4$
• $\text{min} = 9.8$

Now, let's calculate the probability.

$P(13.5 \leq X \leq 17.5) = \frac{17.5 - 13.5}{18.4 - 9.8}$

First, I'll compute the result.The probability that the task will require between 13.5 and 17.5 minutes to perform is approximately 0.47.

Do you need any additional details or have questions about this solution?

Here are 5 related questions for deeper understanding:

1. How do you calculate probabilities for a uniform distribution?
2. What does it mean when a distribution is "uniform"?
3. How would the probability change if the task range was different?
4. Can you visualize the uniform distribution for this task?
5. How do uniform distributions differ from normal distributions?

Tip: For uniform distributions, the probability is simply the ratio of the interval length to the entire range, making calculations straightforward.