SOLUTION: Last year’s freshman class at Big State University totaled 5,331 students. Of those, 1,268 received a merit scholarship to help offset tuition costs their freshman year (although

Question 1196956: Last year’s freshman class at Big State University totaled 5,331 students. Of those, 1,268 received a merit scholarship to help offset tuition costs their freshman year (although the amount varied per student). The amount a student received was N($3,446, $475). If the cost of full tuition was $4,300 last year, what percentage of students who received a merit scholarship did not receive enough to cover full tuition? (Round your answer to the nearest whole percent.)

percent of students _______ %
Answer by proyaop(69) (Show Source): You can put this solution on YOUR website!
**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.

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