Answer :
To find the percentage of male students with heights between 162 cm and 186 cm, standardize the heights to z-scores and use a standard normal distribution table or calculator. Approximately 81.85% of male students will have heights in this range.
The question asks to find the percentage of male students whose height is between 162 cm and 186 cm, given that the heights are normally distributed with a mean of 170 cm and a standard deviation of 8 cm.
First, we need to standardize the given heights by converting them into z-scores using the formula z = (X - (mu)) / (sigma), where X is the height, (mu) is the mean, and (sigma) is the standard deviation.
For the height of 162 cm, the z-score is z = (162 - 170) / 8 = -1. For the height of 186 cm, the z-score is z = (186 - 170) / 8 = 2.
Next, we look up these z-scores in a standard normal distribution table or use a calculator to find the percentage of values between these z-scores. We find that the percentage between a z-score of -1 and 2 is approximately 81.85%.
Therefore, approximately 81.85% of male students will have heights between 162 cm and 186 cm.
