Problem Breakdown:

We are tasked with determining the experimental probability of workers walking to work and predicting the number of workers walking to work in a company of 3600 employees.

---

Part (a): Experimental Probability

The experimental probability is calculated as:

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

Here:

• Number of workers who walk to work = $7$
• Total number of workers surveyed = $80$

$P(\text{walk to work}) = \frac{7}{80}$

Simplify:

$P(\text{walk to work}) = 0.0875 \quad \text{(or } 8.75\% \text{)}$

---

Part (b): Prediction for 3600 Workers

To predict the number of workers walking to work among 3600 employees, we use the probability found in part (a):

$\text{Predicted number} = P(\text{walk to work}) \times \text{Total workers}$

Substitute the values: $\text{Predicted number} = 0.0875 \times 3600$

Calculate: $\text{Predicted number} = 315$

---

Final Answers:

(a) The experimental probability that a randomly selected worker walks to work is 0.0875 (or 8.75%).

(b) Approximately 315 workers out of 3600 are predicted to walk to work.

---

Do you want further details on any step or related concepts? 😊

Related Questions:

1. How does experimental probability differ from theoretical probability?
2. Can we always generalize survey data to larger populations? Why or why not?
3. How do we calculate probabilities for multiple independent events?
4. What are the limitations of using experimental probability for prediction?
5. How would rounding the probability affect the prediction accuracy?

Tip: Always check whether the sample size of a survey is large enough to make generalizations about the entire population.