Answer :
About 95.4% of male students have heights between 154 cm and 186 cm, which is determined by calculating the Z-scores for both height bounds and referring to the standard normal distribution table.
The question asks for the percentage of male students whose height is between 154 cm and 186 cm given that the height is normally distributed with a mean of 170 cm and a standard deviation of 8 cm. To find this percentage, we calculate the Z-scores for both the lower bound (154 cm) and the upper bound (186 cm) and then use the standard normal distribution table to find the probabilities.
To calculate the Z-score for 154 cm:Z = (X - \\(\mu\\)) \\/ \\(\sigma\\), where X is 154 cm, \\(\mu\\) is the mean (170 cm), and \\(\sigma\\) is the standard deviation (8 cm), we get Z = (154 - 170) \\/ 8 = -2. To calculate the Z-score for 186 cm, we use the same formula and get Z = (186 - 170) \\/ 8 = 2.
Using the standard normal distribution table, we find the area between -2 and 2 which is approximately 95.4%. Therefore, about 95.4% of male students have heights between 154 cm and 186 cm.
