Matplotlib plot scale - python-3.x

Question

I want to make a few tools to help to learn and teach basic statistic. One of them aims to help visualise z-score probability table:
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
sns.set_style('whitegrid')
import scipy.stats as st
def draw_z_score(x, cond, mean, std, title,color='b'):
y = st.norm.pdf(x, mean, std)
z = x[cond]
plt.plot(x, y)
plt.ylim(ymin=0)
plt.xlim(xmin=-4.5, xmax=4.5)
plt.fill_between(z, 0, st.norm.pdf(z, mean, std),color=color)
plt.title(title)
plt.tight_layout()
plt.show()
def z_table_probabilty (z_score, z_score2=None, area='l'):
normal = np.arange(-3.9, 3.9, 0.1)
if area == 'l':
Pz = round(st.norm.cdf(z_score), 4)
draw_z_score(normal,normal<z_score,0,1,f'z = {z_score} P(z)={Pz}')
elif area == 'r':
Pz = round(1 - st.norm.cdf(z_score), 4)
draw_z_score(normal,normal>z_score,0,1,f'Z ={z_score} P(1-z)={Pz}',color='r')
elif area == 'tt' and z_score2 != None:
z2 = max(z_score, z_score2)
z = min(z_score, z_score2)
Pz = round(st.norm.cdf(z2) - st.norm.cdf(z), 4)
draw_z_score(normal,(normal<z2)&(normal>z),0, 1, f'z= {z} i z\'= {z2} P(z\'-z)={Pz}', color='y')
Now, when I try:
z_table_probabilty(-0.9)
I have:
z-score=-0.9
Could someone tell my why z-score -0.9 is equal 1 on my plot?, and why the distances between x=4 and end of distribution tail, and x=-4 and end of other tail are different? The whole plot seems to be slightly moved.
What have I done wrong?
Thanks
MV

Answer 1

normal = np.arange(-3.9, 3.9, 0.1) creates an array from -3.9 to 3.8. The end point is not included. Hence you see the curve start at -3.9 and end at 3.8.
With normal<z_score you choose all the points in normal which are smaller than z_score. When z_score=-0.9, those points are from -3.9 to -1.0 because -0.9 is not smaller than -0.9.
In total I would recommend defining normal a bit more dense. This would avoid the two problems. E.g.
normal = np.linspace(-3.9, 3.9, 391)
to create points in steps of 0.02 instead of 0.1.