SOLUTION: The heights of adult men in America are normally distributed, with a mean of 69.3 inches and a standard deviation of 2.68 inches. The heights of adult women in America are also nor

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Question 1197912: The heights of adult men in America are normally distributed, with a mean of 69.3 inches and a standard deviation of 2.68 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.5 inches and a standard deviation of 2.59 inches.
a) If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)?
z =

b) If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)?
z =

c) Who is relatively taller?
-The 5 foot 11 inch American woman
-The 6 foot 3 inch American man
Answer by onyulee(41)   (Show Source): You can put this solution on YOUR website!
**a) Z-score for the 6-foot-3-inch man:**
* **Convert height to inches:** 6 feet 3 inches = 75 inches
* **Calculate z-score:**
z = (x - μ) / σ
z = (75 - 69.3) / 2.68
z ≈ 2.14
**b) Z-score for the 5-foot-11-inch woman:**
* **Convert height to inches:** 5 feet 11 inches = 71 inches
* **Calculate z-score:**
z = (x - μ) / σ
z = (71 - 64.5) / 2.59
z ≈ 2.51
**c) Who is relatively taller?**
* The **woman** is relatively taller.
**Explanation:**
* A higher z-score indicates that the individual is further above the mean of their respective population.
* The woman's z-score of 2.51 is higher than the man's z-score of 2.14, meaning she is further above the average height for women than the man is above the average height for men.
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