assume exam with cohort of normal distribution. 80% of cohort passed, pass mark is alpha, my score 76%. graph the percentile of my score (ie 76%) as y axis, with the alpha on the x axis. mean score of cohort 61%

Here is the graph showing the percentile of your score (76%) against the pass mark (\(\alpha\)) on the x-axis. The x-axis represents different possible pass marks, and the y-axis represents the percentile rank of your score under those conditions.

### Key observations:
- As the pass mark (\(\alpha\)) increases, the percentile rank of your score decreases.
- The red dashed line highlights where the 80th percentile is approximately located on the graph.

Would you like further details or have any questions about this analysis?

### Related Questions:
1. How can we calculate the exact percentile rank for different scores?
2. How does changing the pass percentage (e.g., 70% passed) affect the standard deviation?
3. How does a change in the cohort's mean score influence your percentile?
4. What are the z-scores, and how do they relate to percentile ranks in a normal distribution?
5. How could we estimate the percentile rank if the distribution were not normal?

#### Tip:
Always remember that in a normal distribution, the mean and standard deviation fully define the shape, allowing easy computation of percentiles.

Assume an exam with a cohort of normal distribution. 80% of the cohort passed, the pass mark is alpha, my score is 76%. Graph the percentile of my score (76%) as the y-axis, with the alpha on the x-axis. The mean score of the cohort is 61%.

This problem explores a cohort of normally distributed exam scores, with 80% passing. Learn how to graph the percentile rank of a score (76%) against various pass marks, with a mean cohort score of 61%. Understand key concepts such as normal distribution, Z-scores, and percentile rank calculations.

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