Adult men have an average height of 69.0 inches with a standard deviation of 2.8 inches. Find the height of a man with a z-score of 1.46. Round your answer to one decimal place.
Question
Adult men have an average height of 69.0 inches with a standard deviation of 2.8 inches. Find the height of a man with a z-score of 1.46. Round your answer to one decimal place.
Solution
To find the height of a man with a z-score of 1.46, we need to use the formula for a z-score:
Z = (X - μ) / σ
where: Z is the z-score, X is the value we're trying to find, μ is the mean, and σ is the standard deviation.
We can rearrange the formula to solve for X:
X = Zσ + μ
Substituting the given values:
X = 1.46 * 2.8 + 69.0
X = 4.088 + 69.0
X = 73.088
Rounding to one decimal place, the height of a man with a z-score of 1.46 is 73.1 inches.
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