import pandas as pd 
import numpy as np
import matplotlib.pyplot as plt 
from scipy.stats import gamma 

# generate random data that is not normally distributed
np.random.seed(123)
shape  = 1.0
scale = 50.0 

revenue = gamma.rvs(shape, scale=scale, size=10000)
plt.hist(revenue, bins=100, density=True, alpha=0.6, color='blue');
plt.title("Distribution of Client Revenue")
plt.show();

print("Population Mean: {:.1f}".format(revenue.mean()))

Population Mean: 49.4

num_samples = 10000
sample_size = 100
sample_means = []

for i in range(num_samples):
    random_sample = np.random.choice(revenue, size=sample_size, replace=False)
    sample_means.append(random_sample.mean())

sample_means = pd.Series(sample_means)
plt.hist(sample_means, bins=50, density=True, alpha=0.6, color='blue');
plt.title("Distribution of Sample Mean Revenue")
plt.show();

print("Population Mean: {:.1f}".format(sample_means.mean()))

Population Mean: 49.4