Final answer:
Predicting final exam scores without a specific model is impossible, and the required passing score is not specified in the provided information. The statement about 68 percent of students passing is indicative but not conclusive. Additionally, reference to a 5 percent level of significance suggests a hypothesis testing scenario to validate claims about passing rates.
Step-by-step explanation:
The question pertains to predicting scores for a final exam based on previous exam performance in a distant learning program. The predicted final exam score provided is 261.19, which exceeds the maximum of 200 points possible, indicating an error as the maximum score cannot exceed the total possible points. To address part (a) of the question, with a score of 66 on the third exam, without additional context or a clear predictive model, we cannot provide an accurate prediction. Similarly, for part (b), a score of 90 on the third exam is incomplete information to predict a final exam score without a specific model or correlation data between exam scores.
As for the passing score, the provided information does not directly state what score is required to pass the final exam. However, a passage indicated that 68 percent of students typically pass the final exam according to a professor. If the performance required to pass is consistent with the professor's historical data, then more than two-thirds of students achieve the passing grade, although the exact score needed is not specified. Furthermore, the benchmark scores presented for different levels of achievement in international education standards highlight the variance in performance and do not directly pertain to passing individual course exams.
The issue of predicting final exam scores and whether the provided claimed average passing rates are accurate is reminiscent of hypothesis testing, where at a 5 percent level of significance, one could test if the evidence supports the claim or points to some different conclusion.