Final answer:
To find the height corresponding to a given z-score, use the formula height = mean + (z-score × standard deviation). For a z-score of 1.70, the height is 69.1 inches, while for a z-score of -1.40, the height is 59.8 inches.
Step-by-step explanation:
Calculating Heights from Z-scores
To calculate a person's height based on their z-score, you use the formula height = mean + (z-score × standard deviation).
For a z-score of 1.70, the calculation would be as follows:
Height = 64 + (1.70 × 3) = 64 + 5.1 = 69.1 inches.
This means that a man with a z-score of 1.70 is 69.1 inches tall, which is 1.70 standard deviations above the mean height.
For a z-score of −1.40, the calculation would be:
Height = 64 + (-1.40 × 3) = 64 - 4.2 = 59.8 inches.
This means that a man with a z-score of -1.40 is 59.8 inches tall, which is 1.40 standard deviations below the mean height.