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QuestionStatistics
The dot plot shows the heights of college women. The mean is 64 inches (5 feet 4 inches) and the standard deviation is 3 inches. Complete parts a and b below.
a. What is the z-score for a height of 61 inches?
b. What is the height of a human with a z-score of 3?
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Answer
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Step 1
z = \frac{61 - 64}{3} = \frac{-3}{3} = -1
To find the z-score for a height of 61 inches, we use the formula for calculating z-scores: Plugging these values into the formula, we get:
Final Answer
2. To find the height of a human with a z-score of 3, we rearrange the z-score formula to solve for $x$: x = \mu + z\sigma For part b, $z = 3$, $\mu = 64$ inches, and $\sigma = 3$ inches. Plugging these values into the formula, we get: x = 64 + 3 \times 3 = 64 + 9 = 73
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