Problem 13BSC

Comparing Values. In Exercises, use z scores to compare the given values.

Tallest Man and Woman As of this writing, the tallest living man is Sultan Kosen, who has a height of 247 cm. The tallest living woman is De-Fen Yao, who is 236 cm tall. Heights of men have a mean of 175 cm and a standard deviation of 7 cm. Heights of women have a mean of 162 cm and a standard deviation of 6 cm. Relative to the population of the same gender, who is taller? Explain.

Answer :

Step 1 of 1 :

Tallest Man and Woman As of this writing, the tallest living man is Sultan Kosen, who has a height of 247 cm.

So x = 247

Heights of men have a mean of 175 cm and a standard deviation of 7 cm.

We know that mean and standard deviation

we have to find the Sultan Kosen z-score.

The formula of the z-score is

z =

Substitute x , and values.

z =

z =

z = 10.28

z = 10.29

Therefore Sultan Kosen z-score = 10.29

The tallest living woman is De-Fen Yao, who is 236 cm tall.

So x = 236

Heights of women have a mean of 162 cm and a standard deviation of 6 cm.

Here mean and standard deviation

we have to find the De-Fen Yao z-score.

The formula of the z-score is

z =

Substitute x , and values.

z =

z =

z = 12.33

Therefore De-Fen Yao z-score = 12.33

De Fen Yao is relatively taller, because her z score of 12.33, which is greater than the z score of 10.29 for Sultan Kosen.

De-Fen Yao is more standard deviations above the mean than Sultan Kosen.