Final answer:
To find the percentage of students between 180 cm and 185 cm in height, calculate the z-scores for these values and find the areas under the normal distribution curve using a standard normal distribution table or calculator. The percentage of students between these heights is approximately 13.59%.
Step-by-step explanation:
To find the percentage of students between 180 cm and 185 cm in height, we need to calculate the area under the normal distribution curve between these two values.
First, we need to calculate the z-scores for 180 cm and 185 cm using the formula:
z = (x - mean) / standard deviation
z(180 cm) = (180 - 175) / 5 = 1
z(185 cm) = (185 - 175) / 5 = 2
Next, we can use a standard normal distribution table or a calculator to find the area to the left of each z-score.
The percentage of students between 180 cm and 185 cm in height is the difference between these two areas.
In this case, the area to the left of z = 1 is approximately 0.8413 and the area to the left of z = 2 is approximately 0.9772.
Therefore, the percentage of students between 180 cm and 185 cm in height is approximately 0.9772 - 0.8413 = 0.1359, or 13.59%.