Men have heights with a mean of 176 cm and a standard deviation of 7 cm. Charles Darwin had a height of 182 cm. If we consider "usual" heights to be those that convert to z-scores between -2 and 2, is Darwin's height usual or unusual?

Charles Darwin's height of 182 cm corresponds to a z-score of 0.8571, calculated using the mean height of 176 cm and a standard deviation of 7 cm. Since this z-score is within the 'usual' range of -2 to 2, Darwin's height is considered usual and not unusual.

Explanation:

To determine whether Charles Darwin's height is usual or unusual, we calculate his z-score using the given mean and standard deviation. The formula for the z-score is:

z = (X - μ) / σ

where X is the value in question, μ is the mean, and σ is the standard deviation. For Charles Darwin, the height (X) is 182 cm, the mean (μ) is 176 cm, and the standard deviation (σ) is 7 cm.

Using the formula, we get:

z = (182 - 176) / 7

z = 6 / 7

z = 0.8571

Since a z-score between -2 and 2 is considered usual, and Darwin's z-score is 0.8571, his height is within the usual range. Therefore, Charles Darwin's height is not unusual.