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Suppose that in a large class, the instructor announces that the population mean exam grade is 75 with a population standard deviation of 12. Consider the following two scenarios: + The exam grade of a randomly selected student from the class? Find your random student's datafhere =| + The mean exam grade of a sample of 10 students from the class? Find your random students' data here .. Tasks for Your Initial Posting: 1. Explain Your Reasoning: Based on your understanding of the normal distribution and the Central Limit Theorem, explain which of the two values (a single score or a sample mean of 10) is more likely to be closer to the population average of 75. Why? 2. Calculate z-scores: Show the appropriate formulas to calculate the z-score for each scenario. e Use the individual score or the sample mean as x or Use a = 12 for the population standard deviation e Useag = Va for the standard error in the sample mean e Which z-score is closer to 0? What does that indicate? 3. Construct a 95% Confidence Interval For each scenario (the individual score and the sample mean of 10 students), construct a 95% confidence interval around the observed value