High School

Men have heights with a mean of 176 cm and a standard deviation of 7 cm. Charles Darwin had a height of 182 cm. Convert Darwin's height to a z-score.

Answer :

Charles Darwin's height of 182 cm corresponds to a z-score of approximately 0.8571.

To convert Charles Darwin's height to a z-score, we'll use the formula for z-score:

[tex]\[ z = \frac{x - \mu}{\sigma} \][/tex]

Where:

z is the z-score,

x is the individual height (in this case, Charles Darwin's height of 182 cm),

[tex]\( \mu \)[/tex] is the mean height (176 cm), and

[tex]\( \sigma \)[/tex] is the standard deviation (7 cm).

Substitute the given values into the formula:

[tex]\[ z = \frac{182 - 176}{7} \][/tex]

[tex]\[ z = \frac{6}{7} \][/tex]

[tex]\[ z \approx 0.8571 \][/tex]