Given that the time it takes to mark a set of assignments is uniformly distributed on the interval $[38, 90]$, we can calculate the probability that the next set will take more than 59.06 minutes.

For a uniform distribution, the probability that a random variable $X$ falls within a certain interval $[a, b]$ is given by:

$P(X > x) = \frac{b - x}{b - a}$

where $a = 38$, $b = 90$, and $x = 59.06$.

Calculation:

$P(X > 59.06) = \frac{90 - 59.06}{90 - 38} = \frac{30.94}{52} \approx 0.595$

Rounded to two decimal places:

$P(X > 59.06) \approx 0.60$

Final Answer:

The probability that the next set of assignments will be marked in more than 59.06 minutes is approximately 0.60.

Would you like a detailed explanation of the steps? Here are some related questions:

1. How is the formula for uniform distribution derived?
2. What are some real-life examples of uniform distribution?
3. How does uniform distribution differ from normal distribution?
4. Can this method be applied to non-uniform distributions?
5. How does the interval length affect the probability?

Tip: Always visualize uniform distributions with a simple graph, where the area under the curve represents the probability.