Question 1192313
**1. Determine the Z-score for 95% Confidence:**

* For a 95% confidence level, the Z-score is 1.96.

**2. Calculate the Standard Deviation:**

* Standard Error (SE) = Standard Deviation (σ) / √(sample size)
* 3 = σ / √900
* σ = 3 * √900 
* σ = 3 * 30 
* σ = 90

**3. Determine the Required Sample Size:**

* Margin of Error (E) = 4 
* Z-score = 1.96
* Standard Deviation (σ) = 90

* Formula: n = (Z-score * σ / E)²
* n = (1.96 * 90 / 4)²
* n = (44.1)²
* n = 1944.81

* **Round up to the nearest whole number:** n = 1945

**Therefore, the required sample size to be 95% confident that the population mean is within 4 units of the sample mean is 1945.**