import numpy as np
import scipy.stats as st
import matplotlib.pyplot as plt

X = st.poisson(1.5 / 100 * 48)

# a.
X.pmf(0)

0.4867522559599717

X.cdf(0)

0.4867522559599715

# b.
np.sum(X.pmf(np.arange(6)))

0.9998951831177709

X.cdf(5)

0.9998951831177708

# c.
X = st.poisson(1.5 / 100 * 24)
1 - np.sum(X.pmf(np.arange(3)))

0.00595077061399496

1 - X.cdf(2)

0.00595077061399496

# Why is the answer to part b so big? Is the density at 5 big too?

X.pmf(5)

0.0007848546020606052

1.5 / 100 * 48

0.72

x = np.arange(10)
plt.scatter(x, X.pmf(x))