What is the 80th percentile of a distribution that is approximately normally distributed with a population mean of 75 and variance of 16?
A) Approximately 72%
B) Approximately 78%
C) Approximately 84%
D) Approximately 95%

Question

Quizplus · Accepted Answer

The 80th percentile of a normally distributed population can be found using the Z-score associated with the 80th percentile, which is approximately 0.84. Using the formula for converting Z-scores to raw scores (X = μ + Zσ), where μ is the mean (75) and σ is the standard deviation (√variance = √16 = 4), we get X = 75 + (0.84)(4) = 75 + 3.36 = 78.36, which is approximately 78%.

What Is the 80th Percentile of a Distribution That Is