Gpa Highest Percentile
1. **State the problem:** We need to find the GPA cutoff for the highest 2.5% of students, given that GPAs are normally distributed with mean $\mu = 2.9$ and standard deviation $\sigma = 0.6$.
2. **Understand the problem:** The highest 2.5% corresponds to the 97.5th percentile of the normal distribution.
3. **Find the z-score for the 97.5th percentile:** From the standard normal distribution table, the z-score corresponding to 0.975 is approximately $z = 1.96$.
4. **Use the z-score formula:**
$$x = \mu + z \sigma$$
5. **Calculate the GPA cutoff:**
$$x = 2.9 + 1.96 \times 0.6 = 2.9 + 1.176 = 4.076$$
6. **Interpret the result:** The GPA cutoff for the highest 2.5% is approximately **4.08**, so students with GPAs of about 4.1 or higher are in the top 2.5%.
**Final answer:** The GPA cutoff of the highest 2.5% is approximately $4.1$.