First make a grouper:
import pandas as pd
In [1]: grouper = pd.Grouper(freq="1M")
Then make your new column:
In [2]: df['normed'] = df.groupby(grouper).transform(lambda x: x/x.mean())
By passing grouper to the groupby
method you group your data into one month chunks. Within each chunk you divide the 15 minute interval datum by the mean for that month.