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The average time taken to complete an exam, X, follows a normal probability distribution with mean = 60 minutes and standard deviation 30 minutes.
-By what time should 67% of the students have finished the exam? (i.e. What is the 67^th percentile for X?)

Question

Quizplus · Accepted Answer

The 67th percentile in a normal distribution corresponds to a Z-score of approximately 0.44 (from Z-tables or standard normal distribution tables). Using the formula for converting Z-scores to raw scores: X = μ + Zσ, where μ is the mean, σ is the standard deviation, and Z is the Z-score, we get X = 60 + 0.44(30) = 60 + 13.2 = 73.2 minutes.

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