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To solve this problem, we need to calculate the probability that washing dishes will take between 9 and 11 minutes, given that the time is uniformly distributed between 8 and 16 minutes.

For a uniform distribution, the probability density function (PDF) is constant across the range, calculated as follows:

1. **Determine the range of the distribution:**
   - Minimum time (\(a\)) = 8 minutes
   - Maximum time (\(b\)) = 16 minutes
   - Total range = \( b - a = 16 - 8 = 8 \) minutes

2. **Calculate the probability for the interval [9, 11] within [8, 16]:**
   - The length of the interval we are interested in (from 9 to 11) is \(11 - 9 = 2\) minutes.

3. **Calculate the probability:**
   \[
   \text{Probability} = \frac{\text{Length of desired interval}}{\text{Total range}} = \frac{2}{8} = 0.25
   \]

So, the probability that it will take between 9 and 11 minutes to wash the dishes is **0.25** (or 25%).

Would you like further explanation on this topic? 

Here are some related questions you might find helpful:
1. How is a uniform distribution defined mathematically?
2. What is the formula for probability in a uniform distribution?
3. How would you calculate the mean and variance for a uniform distribution?
4. How would this problem change if the distribution were not uniform?
5. How can this approach apply to other real-life problems?

**Tip:** In uniform distribution problems, always start by determining the range, then calculate the probability as the fraction of the interval of interest over the entire range.

The time it takes me to wash the dishes is uniformly distributed between 8 minutes and 16 minutes. What is the probability that washing dishes tonight will take me between 9 and 11 minutes?

Find out how to calculate the probability of washing dishes within a specific time frame using a uniform distribution between 8 and 16 minutes. This example illustrates probability concepts suitable for Grades 10-12.

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