Final answer:
To find the height of the shortest man in the top 10%, we need to determine the z-score that corresponds to the top 10% of the distribution. Using the z-score formula and the given mean and standard deviation, we can calculate the height of the shortest man to be approximately 76.1 inches.
Step-by-step explanation:
To find the height of the shortest man in the top 10%, we need to determine the z-score that corresponds to the top 10% of the distribution. The formula for the z-score is:
z = (X - μ) / σ
where X is the given height, μ is the mean height, and σ is the standard deviation. Rearranging the formula to solve for X, we have:
X = μ + z * σ
Since we want the height of the shortest man, we need to find the z-score that corresponds to the top 10% of the distribution. Using a z-table or a calculator, we find that the z-score for the top 10% is approximately 1.28. Plugging this value into the formula, we get:
X = 73.4 + 1.28 * 2.7 = 76.076 inches
Therefore, the height of the shortest man in the top 10% is approximately 76.1 inches.