The heights of women aged 20 to 29 in a country are approximately Normal with me
ID: 3298860 • Letter: T
Question
The heights of women aged 20 to 29 in a country are approximately Normal with mean 64.2 inches and standard deviation 2.8 inches. Men the same age have mean height 69.3 inches with standard deviation 3.0 inches. What is the z-score for a woman 6 feet tall? (Round your answer to two decimal places.)
1
What is the z-score for a man 6 feet tall? (Round your answer to two decimal places.)
2
Say in simple language what information the z-scores give that the original nonstandardized heights do not.
The z-scores show us how the subjects compare to the average subject within their gender group. The deviation from the mean is measured in units of standard deviations. In the present case the man is slightly taller than average, while the woman is much taller than average
The z-scores show us how the subjects compare to the standard deviation. The deviation from the standard deviation is measured in the same units as the actual data, in this case inches. In the present case the man is slightly taller than average, while the woman is much taller than average.
The z-scores don't give us any additional information, since we already know that the man and woman have equal heights.
The z-scores show us how the subjects compare to the average subject. The deviation from the mean is measured in the same units as the actual data, in this case inches. In the present case the man is slightly taller than average, while the woman is much taller than average.
Explanation / Answer
1) the z-score for a woman
x= 6 feet =72 inches
Hence,
z = (x-u)/sigma
= (72-64.2)/2.8
= 2.785714285 =~~= 2.79
2) the z-score for a man
6 feet =72 inches
z = (x-u)/sigma
= (72-69.3)/3
= 0.90
3)
It lets you compare the raw score to the other scores in the population. The actual high does not do this.
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