Can you alter a CDF once data gets observed?

Question

In python from the package (scipy.stats) I'm fitting some distribution to a dataset over how early schoolkids will arive for school.

def gumbel_r_distribution(data):
    loc, scale = scipy.stats.gumbel_r.fit(data)
    distribution = scipy.stats.gumbel_r(loc=loc, scale=scale)

Now that i have the distribution, and a number of how many students will arive, lets say n=100, I can obtain the CDF by calling

cdf = distribution.cdf

This CDF can thus tell me that i.e. 10% of students will have arrived $\bigg(\int_{-\infty}^{30}$ cdf$\bigg)$ 30 minutes early. Thus we have $0.1*n=10$ students.

Now I have an ongoing observation to an experiment. At 30 minutes early, we have 15 students who arrived, however my n=100 is unchanged, can I in some way alter my CDF thus that it fits the data so far in the current experiment?