Imagine a population consisting of 1,500 values that are normally distributed around a mean of 60, which exhibits a standard deviation of 8. The 75th percentile most closely corresponds to which value of Z?

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Quizplus · Accepted Answer

The 75th percentile in a normal distribution corresponds to a Z-score of approximately 0.674 (from Z-tables or standard normal distribution tables). To find the corresponding value in the population, use the formula: X = μ + Zσ, where μ is the mean, σ is the standard deviation, and Z is the Z-score. Substituting the given values: X = 60 + 0.674(8) = 60 + 5.392 = 65.392, which is closest to 65.4.

Imagine a Population Consisting of 1,500 Values That Are Normally