Solution:

Part a: Experimental Probability

The experimental probability $P$ is calculated as the ratio of the number of workers who walk to work to the total number of workers surveyed:

$P = \frac{\text{Number of workers who walk to work}}{\text{Total number of workers surveyed}}$

Substitute the values:

$P = \frac{41}{160}$

Simplify:

$P = 0.25625$

So, the experimental probability is 0.25625 or approximately 25.63%.

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Part b: Predict the number of workers out of 4500 who walk to work

To predict the number of workers who walk to work, use the experimental probability and multiply it by the total number of workers:

$\text{Predicted number of workers} = P \times \text{Total number of workers in the company}$

Substitute the values:

$\text{Predicted number of workers} = 0.25625 \times 4500$

Perform the calculation:

$\text{Predicted number of workers} = 1153.125$

Rounding to the nearest whole number:

$\text{Predicted number of workers} = 1153$

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Final Answers:

a. The experimental probability that a randomly selected worker walks to work is 0.25625 (approximately 25.63%).

b. About 1153 workers are predicted to walk to work out of 4500.

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Would you like further explanation on any step or a different approach?
Here are 5 related questions you might find interesting:

1. How would the prediction change if the probability increased to 30%?
2. What is the probability that a randomly selected worker does not walk to work?
3. If the survey included 500 workers and 150 walked to work, what would the new probability be?
4. How would a sample size change (e.g., 200 workers) affect the accuracy of predictions?
5. Could this prediction method work for other forms of commuting, like cycling?

Tip: Experimental probability becomes more accurate with larger sample sizes!