import numpy as np
import matplotlib.pyplot as plt
import scipy as sp

# 1
m = 50_000
s = 2_000
X = sp.stats.norm(loc = m, scale = s)

# 1a
X.cdf(48_000)

0.15865525393145707

X.ppf(.9)

52563.1031310892

# made up question
# How much probability does 
# this distribution put over negative numbers?
X.cdf(0)

3.056696706382561e-138

# How much probability lives between 
# 4 sigma of mu?
X.cdf(m + 4 * s) - X.cdf(m - 4 * s)

0.9999366575163338

ss = np.linspace(0, 10, 100)
p = X.cdf(m + ss * s) - X.cdf(m - ss * s)
plt.plot(ss, p);

# 1
X = sp.stats.norm(loc = 10, scale = 2)

# 1a
X.cdf(12) - X.cdf(8)

0.6826894921370859

1 - X.cdf(14)

0.02275013194817921

#3
X = sp.stats.norm(loc = 5.2, scale = 0.8)

#3a
X.cdf(4)

0.06680720126885806

# 3b
1 - X.cdf(6)

0.15865525393145707

X.ppf(.9)

6.225241252435681