The SAT scores $(x)$ of Florida high school students are normally distributed with mean $\mu=1,308$ and standard deviation $\sigma=94$. Top $33 \%$ of these students are expected to get full tuition scholarship. What is the minimum score for this scholarship?

Step 1 ：The SAT scores of Florida high school students are normally distributed with mean \(\mu=1,308\) and standard deviation \(\sigma=94\). The top 33% of these students are expected to get a full tuition scholarship. We need to find the minimum score for this scholarship.

Step 2 ：This is a question about the normal distribution. The mean and standard deviation of the scores are given, and we need to find the score that corresponds to the 67th percentile (since the top 33% corresponds to the bottom 67%).

Step 3 ：We can use the z-score formula, which is: \[z = \frac{x - \mu}{\sigma}\] where: \(z\) is the z-score, \(x\) is the value from the dataset, \(\mu\) is the mean of the dataset, and \(\sigma\) is the standard deviation of the dataset.

Step 4 ：We can rearrange this formula to solve for \(x\): \[x = z\sigma + \mu\]

Step 5 ：We can use a z-table to find the z-score that corresponds to the 67th percentile. The z-score is approximately 0.4399131656732339.

Step 6 ：Substituting the values into the formula, we get: \[x = 0.4399131656732339 \times 94 + 1308\]

Step 7 ：Solving the equation, we find that the minimum score for the scholarship is approximately 1349.35. This means that students need to score at least this much to be in the top 33% and be eligible for the full tuition scholarship.

Step 8 ：Final Answer: The minimum score for the scholarship is approximately \(\boxed{1349.35}\).