The mean height of a population of girls aged 15 to 19 years in a northern province in Sweden was found to be 165 cm with a standard deviation of 15 cm. Assuming that the heights are normally distributed, find the heights in centimeters that correspond to the following percentiles:

a. Between the 20th and 50th percentiles.

b. Between the 40th and 60th percentiles.

c. Between the 10th and 90th percentiles.

d. Above the 80th percentile.

e. Below the 10th percentile.

f. Above the 5th percentile.