At the end of a quarter, Carol took four final exams. The mean and standard deviation for each exam along with Carol's grade on each exam are listed below. Assume that the grades on each exam are normally distributed. Exam Mean Standard Deviation Carol's Grade Language 75 6.3 78 History 85 4.1 83 Psychology 88 3.5 89 Statistics 70 8.6 83 a. On which exam did Carol do best relative to the other students taking the exam? b. What was her percentile rank on this exam?
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The Z-score is calculated using the formula: \[ Z = \frac{X - \mu}{\sigma} \] where \( X \) is Carol's grade, \( \mu \) is the mean, and \( \sigma \) is the standard deviation. - **Language:** \[ Z = \frac{78 - 75}{6.3} = \frac{3}{6.3} \approx 0.48 \] - Show more…
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