SOLUTION: The heights of adult men in America are normally distributed, with a mean of 69.2 inches and a standard deviation of 2.65 inches. The heights of adult women in America are also nor
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Question 1177014: The heights of adult men in America are normally distributed, with a mean of 69.2 inches and a standard deviation of 2.65 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.7 inches and a standard deviation of 2.54 inches.
If a man is 6 feet 3 inches tall, what is his z-score (to 4 decimal places)?
z =
If a woman is 5 feet 11 inches tall, what is her z-score (to 4 decimal places)?
z =
Who is relatively taller?
The 6 foot 3 inch American man
The 5 foot 11 inch American woman Answer by CPhill(1959) (Show Source):
You can put this solution on YOUR website! Here's how to calculate the z-scores and determine who is relatively taller:
**1. Convert Heights to Inches**
* Man: 6 feet 3 inches = (6 * 12) + 3 = 75 inches
* Woman: 5 feet 11 inches = (5 * 12) + 11 = 71 inches
**2. Calculate Z-scores**
* **Man's z-score:**
* z = (x - μ) / σ
* z = (75 - 69.2) / 2.65
* z = 5.8 / 2.65
* z ≈ 2.1887
* **Woman's z-score:**
* z = (x - μ) / σ
* z = (71 - 64.7) / 2.54
* z = 6.3 / 2.54
* z ≈ 2.4803
**3. Determine Who is Relatively Taller**
* The woman has a higher z-score (2.4803) than the man (2.1887).
* This means the woman's height is further above the average height for women than the man's height is above the average height for men.
**Answers**
* Man's z-score: 2.1887
* Woman's z-score: 2.4803
* Who is relatively taller? The 5 foot 11 inch American woman
