The heights of adult males are approximately Normally distributed with a mean of 70 inches and a standard deviation of 3 inches. An adult male is categorized as "short" if he is less than 64 inches tall and categorized as "tall" if he is in the top 3% of adult males in terms of height.
How tall does an adult male need to be to be assigned to the "tall" category?

Question

Quizplus · Accepted Answer

To find the height that categorizes an adult male as "tall" (top 3%), we use the Z-score formula for the normal distribution. The Z-score corresponding to the top 3% is approximately 1.88 (since the area to the left of this Z-score is about 0.97 or 97%, leaving 3% in the right tail). Using the formula for converting Z-scores to raw scores: X = μ + Zσ, where μ is the mean (70 inches), σ is the standard deviation (3 inches), and Z is the Z-score (1.88), we get X = 70 + (1.88)(3) = 70 + 5.64 = 75.64 inches.

The Heights of Adult Males Are Approximately Normally Distributed with a Mean