Final answer:
To find the percentage of students with an arm span of at least 170 cm, calculate the z-score and use a standard normal distribution table or calculator to find the percentage of values to the right of the z-score.
Step-by-step explanation:
The percentage of students with an arm span of at least 170 cm can be found by calculating the area under the curve of a normal distribution.
First, find the z-score for a height of 170 cm using the formula:
z = (x - μ) / σ
Where x is the height, μ is the mean, and σ is the standard deviation.
Next, use a standard normal distribution table or calculator to find the percentage of values to the right of the z-score. This represents the percentage of students with an arm span of at least 170 cm.
For example, if the mean arm span is 165 cm and the standard deviation is 5 cm, the z-score would be:
z = (170 - 165) / 5 = 1
Using a standard normal distribution table, approximately 84% of values are to the left of a z-score of 1. Therefore, about 16% of students would have an arm span of at least 170 cm.