Response to Richard Crandall
Your discussion accurately points out the importance of the normal distribution. It emphasizes the importance of the central limit theorem in random variables. However, you argue that the usage of the normal distribution in grading is comparable to awarding grades rather than students earning them. Don’t you think that when the grades of an exam fail to form a normal distribution with minimal outliners, raises the possibility of a fault in the testing mechanism? Such defects may include, a hard exam, poor knowledge transfer to the students, and lack of preparedness. As such, the result failing to form a normal distribution curve should initiate a corrective measure in the learning process.
Response to Bradd Baldwin
Your approach to the discussion is quite captivating. Your response highlights the possible merits and demerits of grading on a curve. On your vote for grading on a curve, you are keen to explain the potential benefits that include the professors' review of the students’ performance and interrogating why they perform in a particular pattern. As such, the professor can easily revisit missed concepts. However, you also mention that the full reliance on grading on a curve makes the learners relax. They know that they will defiantly pass irrespective of their efforts. Although it is debatable, the adjustment of the students' scores may likely affect their perception of exams compared to correcting the teaching and testing mechanisms.
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Response to Andres Alvarez
I agree with your observation that the trucks manager's construction of the confidence interval is somewhat correct. You, however, fail to state that the manager fails to express the degree of confidence in his inference as you accurately put it in (b). You further explain why you think it is prudent to construct the confidence interval. It is beneficial in saving the time of analyzing data because a representative sample is used. It is also prudent to point out that assuming that the sample was approaching normal distribution is accurate. As such, the central limit theorem applies and warrants for a sample size bigger than 30. Finally, confidence interval estimation is very applicable in sampling aircraft system failures.
Response to Benjamin Washburn
I agree with your disapproval of the truck manager’s reasoning. It is inaccurate to conclude that the confidence interval contains the mean operating cost of the entire fleet. The correct interpretation would have been that there is a 95% chance that the interval of $253 to $ 320 contains the mean operating cost of the entire fleet. It further points to the statistical inference flaw that the manager made as opposed to small sample size you state in your discussion since we are not informed what the total number of trucks in the fleet. However, assuming that the fleet is large way above 30, it is prudent to use a sample size of above 30. The fleet manager has an idea of the importance of the confidence interval. It is also evident that is applicable as used in the verification of invoices while performing CPA audits.
