Kyle and Ryan take entrance exams at two different universities. Kyle scores a 476 on an exam with a mean of 380 and a standard deviation of 68 , while Ryan scores a 38 on an exam with a mean of 25 and a standard deviation of.4.5. Which do you think is more likely to be accepted at the university of his choice? Kyle Ryan

To determine who is more likely to be accepted to their chosen university, we can compare Kyle's and Ryan's exam scores relative to the distributions of their respective exams. This can be done by calculating their **z-scores**, which indicate how many standard deviations each score is from the mean. ### Calculating the Z-Scores 1. **Kyle's Z-Score:** - **Score:** 476 - **Mean (μ):** 380 - **Standard Deviation (σ):** 68 - **Z-Score Formula:** \( z = \frac{(X - \mu)}{\sigma} \) - **Calculation:** \[ z = \frac{(476 - 380)}{68} = \frac{96}{68} \approx 1.41 \] 2. **Ryan's Z-Score:** - **Score:** 38 - **Mean (μ):** 25 - **Standard Deviation (σ):** 4.5 - **Z-Score Formula:** \( z = \frac{(X - \mu)}{\sigma} \) - **Calculation:** \[ z = \frac{(38 - 25)}{4.5} = \frac{13}{4.5} \approx 2.89 \] ### Interpretation - **Kyle's z-score of 1.41** means he scored **1.41 standard deviations above the mean** for his exam. - **Ryan's z-score of 2.89** means he scored **2.89 standard deviations above the mean** for his exam. A higher z-score indicates a better performance relative to the peer group taking the same exam. Ryan's z-score is significantly higher than Kyle's, suggesting that Ryan performed exceptionally well compared to his peers. ### Conclusion **Ryan** is more likely to be accepted to the university of his choice, as his exam score places him further above the average compared to Kyle's performance.