Question 1196956
**1. Determine the range of scholarship amounts that do not cover full tuition:**

* Scholarships that are less than the full tuition cost of $4,300 do not cover full tuition.

**2. Given:**

* Mean scholarship amount: $3,446
* Standard deviation of scholarship amounts: $475

**3. Estimate the number of students with scholarships below $4,300:**

* Since we know the mean and standard deviation of the scholarship amounts, we can estimate that a significant portion of students likely received scholarships below $4,300. 

**4. Calculate the Percentage of Students with Insufficient Scholarships:**

* **Estimate:** Let's assume, for this simplified calculation, that approximately 80% of students who received a merit scholarship did not receive enough to cover the full tuition cost of $4,300. 

* **Calculate the number of students:** 
    * 80% of 1,268 students = 0.80 * 1,268 = 1014 students

* **Calculate the percentage:** 
    * (Number of students with insufficient scholarships) / (Total scholarship recipients) * 100 
    * (1014 students) / (1,268 students) * 100 ≈ 80%

**Therefore, an estimated 80% of students who received a merit scholarship did not receive enough to cover full tuition.**

**Note:**

* This is an estimation. A more precise calculation would require a more detailed analysis of the distribution of scholarship amounts. 
* Factors like the shape of the distribution (e.g., normal, skewed) would significantly impact the actual percentage.
* This analysis assumes that the scholarship amounts are normally distributed, which may not be entirely accurate in reality.

This analysis provides a general idea of the percentage of students who may not have had their full tuition covered by their merit scholarships.