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To find the 75th percentile salary for male professors, we can use the information provided:

1. **Average (mean) salary**: $99,685
2. **Standard deviation**: $5,200
3. **Percentile**: 75th

For a normally distributed dataset, the 75th percentile corresponds to a Z-score of approximately 0.674 (from standard normal distribution tables).

We’ll use the formula for a percentile in a normal distribution:
\[
X = \mu + Z \cdot \sigma
\]
where:
- $ \mu $ is the mean,
- $ Z $ is the Z-score for the 75th percentile (0.674),
- $ \sigma $ is the standard deviation.

### Calculations
1. Substitute values:
   \[
   X = 99685 + (0.674 \times 5200)
   \]
2. Calculate:
   \[
   X = 99685 + 3504.8 = 103189.8
   \]
3. Round to the nearest dollar:
   \[
   X \approx 103190
   \]

### Answer
The 75th percentile salary for male professors is **$103,190**.

Would you like more detailed steps or have any questions?

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**Related Questions:**
1. How do we find the Z-score for different percentiles?
2. What other percentiles can be calculated with this data?
3. How does changing the standard deviation affect the percentile result?
4. Can you explain why a normal distribution is used in this context?
5. How would we calculate percentiles for a skewed distribution?

**Tip:** Knowing the Z-scores for common percentiles (like 50th, 75th, 90th) can speed up calculations.

The average salary of a male full professor at a public four-year institution offering classes at the doctoral level is $99,685. For a female full professor at the same kind of institution, the salary is $90,330. If the standard deviation for the salaries of both genders is approximately $5,200 and the salaries are normally distributed, find the 75th percentile salary for male professors.

Calculate the 75th percentile salary for male full professors at a public four-year institution with a mean salary of $99,685 and standard deviation of $5,200. This problem involves normal distribution and percentile calculation, suitable for college-level statistics students.

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