One of the tallest living men has a height of 263 cm. One of the tallest living women is 245 cm tall. Heights of men have a means of 177 cm and a standard deviation of 8 cm. Heights of women have a mean of 163 cm and a standard deviation of 4cm. Relative to the population of the same gender, who is taller? Explain
Help please, I'm lost on this subject
Z = (score-mean)/SD
Which one has the largest positive Z score?
To determine who is taller relative to the population of the same gender, we need to calculate the z-scores for both individuals and compare them.
A z-score measures how many standard deviations above or below the mean an individual's measurement falls. It allows us to compare measurements from different populations by standardizing them.
For the tallest living man:
Height = 263 cm
Mean height for men = 177 cm
Standard deviation for men = 8 cm
To calculate the z-score for the tallest living man, we use the formula:
z = (X - μ) / σ
where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.
z_men = (263 - 177) / 8
z_men = 86 / 8
z_men ≈ 10.75
For the tallest living woman:
Height = 245 cm
Mean height for women = 163 cm
Standard deviation for women = 4 cm
To calculate the z-score for the tallest living woman:
z_women = (245 - 163) / 4
z_women = 82 / 4
z_women = 20.5
The z-scores indicate the number of standard deviations each individual's height is from the mean of their respective gender populations. The greater the absolute value of the z-score, the farther the individual's height is from the mean.
Comparing the z-scores, we see that the z-score for the tallest living woman (z_women = 20.5) is much greater than the z-score for the tallest living man (z_men ≈ 10.75).
Therefore, in terms of their respective populations, the tallest living woman is relatively taller than the tallest living man.