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Determining Who Scored Best: Larry, Moe, Curly Exam Scores and Eleanor's College Tests

In this analysis, we examine the exam scores of Larry, Moe, and Curly in their respective classes—History, Philosophy, and Literature—using z-scores to determine who performed best among their classmates. Additionally, we evaluate Eleanor's math scores on the SAT and ACT by converting them to standardized z-scores, facilitating a comparison to identify her best score. Understanding z-scores allows for an accurate assessment against class means and deviations, ultimately revealing the top performers among the students.

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Determining Who Scored Best: Larry, Moe, Curly Exam Scores and Eleanor's College Tests

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  1. Who Did the Best? Larry, Moe and Curly each took an exam in their respective classes, History, Philosophy and Literature. The scores each received are given below. In relationship to the rest of the students in their class who did the best?

  2. Z-Scores • The population z-score is calculated using the population mean and population standard deviation • The population z-score is calculated using the population mean and population standard deviation • The sample z-score is calculated using the sample mean and sample standard deviation

  3. Eleanor took two different college entrance exams, the SAT and the ACT. Her math score on the SAT was 680 and a 27 on the ACT. She wants to send in the best score but she doesn’t know which is the best score. • The distribution of SAT and ACT scores are considered to be normal. The SAT scores had a mean of 500 and a standard deviation of 100. For the ACT the mean is 18 and a standard deviation of 6. Convert both of these scores to the standardized z values and answer the question.

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