Answer :
To find the percentage of male students above 186 cm, we calculate a Z-score of 2 for that height and use a normal distribution table to get the probability. The result indicates that approximately 2.28% of male students are taller than 186 cm.
The student asked to find the percentage of male students whose height is above 186 cm, given that the heights are normally distributed with a mean of 170 cm and standard deviation of 8 cm.
To find this percentage, we will use the Z-score formula:
Z = (X - (mu)) / (sigma)
Where X is the value in question (186 cm), (mu) is the mean (170 cm), and (sigma) is the standard deviation (8 cm). Calculating the Z-score for 186 cm:
Z = (186 - 170) / 8 = 16 / 8 = 2
Now, we look up the Z-score of 2 in the standard normal distribution table. This gives us the probability of a student being shorter than 186 cm. To find the probability of a student being taller, we subtract this value from 1.
For a Z-score of 2, the table gives us a probability of 0.9772. Thus, the percentage of students taller than 186 cm is
1 - 0.9772 = 0.0228 or 2.28%
Therefore, approximately 2.28% of male students are above 186 cm in height.
