We can start by using the standard normal distribution to find the z-scores for the two heights:
z1 = (176 - 180) / 4 = -1
z2 = (180 - 180) / 4 = 0
Then, we can use a standard normal distribution table or a calculator to find the area under the curve between these two z-scores. From a table, we find that the area to the left of -1 is 0.1587 and the area to the left of 0 is 0.5. Therefore, the area between -1 and 0 is:
0.5 - 0.1587 = 0.3413
To find the percentage of the population, we can convert this decimal to a percentage by multiplying by 100:
0.3413 x 100 = 34.13%
Therefore, approximately 34.13% of the population would lie between 176cm and 180cm in height.