Question
A group of 50 students took a test, and their scores
were normally distributed with a mean of 75 and a standard deviation of 10. What is the minimum score needed to be in the top 10% of the class?Solution
To be in the top 10% of the class, a student's score must be higher than 90% of the other scores. Using the standard normal distribution table, we can find that the z-score for the 90th percentile is 1.28. Using the z-score formula, we can find the minimum score needed to be in the top 10% of the class: x = mean + (z-score x standard deviation) = 75 + (1.28 x 10) = 87.8. Therefore, the minimum score needed to be in the top 10% of the class is 87.8.
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