The distance (in km) of 40 engineers from their residence to their place of work were found as follows:
5 3 10 20 25 11 13 7 12 31 19 10 12 17 18 11 32 17 16 2 7 9 7 8 3 5 12 15 18 3 12 14 2 9 6 15 15 7 6 12
What is the empirical probability that an engineer lives:
within `1/2` km from her place of work?

Answer

To find the empirical probability that an engineer lives within 0.5 km from her place of work, we will follow these steps:

### Step 1: Understand the Problem
We need to determine how many engineers live within a distance of 0.5 km from their workplace based on the given data.

### Step 2: List the Distances
The distances of the 40 engineers from their residence to their workplace are:
5, 3, 10, 20, 25, 11, 13, 7, 12, 31, 19, 10, 12, 17, 18, 11, 32, 17, 16, 2, 7, 9, 7, 8, 3, 5, 12, 15, 18, 3, 12, 14, 2, 9, 6, 15, 15, 7, 6, 12

### Step 3: Count the Total Outcomes
The total number of engineers is given as 40.

### Step 4: Identify Favorable Outcomes
Next, we need to count how many engineers live within 0.5 km from their workplace. Since 0.5 km is less than 1 km, we are looking for any distances that are less than or equal to 0.5 km.

Upon reviewing the list of distances, we find that there are no distances equal to or less than 0.5 km.

### Step 5: Calculate the Probability
Using the formula for empirical probability:
\[ \text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} \]
In this case:
- Number of favorable outcomes = 0 (since no engineer lives within 0.5 km)
- Total outcomes = 40

Thus, the probability is:
\[ \text{Probability} = \frac{0}{40} = 0 \]

### Conclusion
The empirical probability that an engineer lives within 0.5 km from her place of work is **0**.

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