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Answer :
The fraction of women above a man's average height is approximately Option E: 1%.
How to find the percentage from the z-score?
To find the fraction of women above a man's average height, we need to calculate the probability that a woman's height is greater than the average height of men.
Using the z-score formula:
z = (x - μ) / σ
where:
x = raw score = 68 inches
μ = mean = 63 inches
σ = standard deviation = 2 inches
Calculating the z-score:
z = (68 - 63) / 2
z = 2.5
Using a standard normal distribution table or calculator, we can find the probability corresponding to a z-score of 2.5.
Looking up the probability for z > 2.5, we find that it is approximately 0.0062097, which is equivalent to 0.62%.
Therefore, the fraction of women above a man's average height is approximately 0.62%, which is closest to answer choice E. 1%.
Complete question is:
Suppose the average man's height is 68 inches, with a standard deviation of 3 inches, and is normally distributed. Also suppose that the average woman's height is 63 inches, with a standard deviation of 2 inches, and is normally distributed. What fraction of women are above a MAN'S average height? (Remember to pick the closest answer.) A. 10% B. 5% C. 3% D. 2% E. 1%
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