How to find the probability from a normal probability density function in python?

Question

Basically, I have plotted a normal curve by using the values of mean and standard deviation. The y-axis gives the probability density.

How do I find the probability at a certain value "x" on the x-axis? Is there any Python function for it or how do I code it?

Answer 1

Not very sure if you mean the probability density function, which is:

given a certain mean and standard deviation. In python you can use the stats.norm.fit to get the probability, for example, we have some data where we fit a normal distribution:

from scipy import stats
import seaborn as sns
import numpy as np
import matplotlib.pyplot as plt

data = stats.norm.rvs(10,2,1000)

x = np.linspace(min(data),max(data),1000)
mu, var = stats.norm.fit(data)
p = stats.norm.pdf(x, mu, std)

Now we have estimated the mean and standard deviation, we use the pdf to estimate probability at for example 12.5:

xval = 12.5
p_at_x = stats.norm.pdf(xval,mu,std)

We can plot to see if it is what you want:

fig, ax = plt.subplots(1,1)
sns.distplot(data,bins=50,ax=ax)
plt.plot(x,p)
ax.hlines(p_at_x,0,xval,linestyle ="dotted")
ax.vlines(xval,0,p_at_x,linestyle ="dotted")