Question 1178708
Let's solve this problem step-by-step:

**Part (a) Estimate the Percentage:**

1.  **Calculate the Sample Proportion (p̂):**
    * p̂ = (Number of workers using public transport) / (Total number of workers)
    * p̂ = 214 / 946
    * p̂ ≈ 0.2262156448

2.  **Convert to Percentage:**
    * Percentage = p̂ * 100%
    * Percentage ≈ 0.2262156448 * 100%
    * Percentage ≈ 22.62156448%

3.  **Round to Four Significant Digits:**
    * Percentage ≈ 22.62%

**Answer:** 22.62

**Part (b) 95% Confidence Interval:**

1.  **Calculate the Standard Error (SE):**
    * SE = √[p̂(1 - p̂) / n]
    * SE = √[0.2262(1 - 0.2262) / 946]
    * SE = √[0.2262(0.7738) / 946]
    * SE = √[0.17499956 / 946]
    * SE = √0.00018498896
    * SE ≈ 0.0136

2.  **Find the Z-score for a 95% Confidence Interval:**
    * For a 95% confidence interval, the z-score is 1.96.

3.  **Calculate the Margin of Error (ME):**
    * ME = z * SE
    * ME = 1.96 * 0.0136
    * ME ≈ 0.026656

4.  **Calculate the Confidence Interval:**
    * Lower Bound: p̂ - ME = 0.2262 - 0.026656 ≈ 0.199544
    * Upper Bound: p̂ + ME = 0.2262 + 0.026656 ≈ 0.252856

5.  **Convert to Percentages:**
    * Lower Bound: 0.199544 * 100% ≈ 19.9544%
    * Upper Bound: 0.252856 * 100% ≈ 25.2856%

6.  **Round to Four Significant Digits:**
    * Lower Bound: 19.95%
    * Upper Bound: 25.29%

**Answer:** (19.95, 25.29)