Sampling from a entire and biased population in Python

import numpy as np  # for sampling for the distributions
import matplotlib.pyplot as plt  # for basic plotting
import seaborn as sns  # for plotting of the histograms

'''
Sampling from a Biased Population
In this tutorial we will go over some code that recreates the visualizations in the Interactive Sampling Distribution Demo.
This demo looks at a hypothetical problem that illustrates what happens when we sample from a biased population and
not the entire population we are interested in.
'''
# Recreate the simulations from the video
mean_uofm = 155
sd_uofm = 5
mean_gym = 185
sd_gym = 5
gymperc = .3
totalPopSize = 40000

# Create the two subgroups
uofm_students = np.random.normal(
    mean_uofm, sd_uofm, int(totalPopSize * (1 - gymperc)))
students_at_gym = np.random.normal(
    mean_gym, sd_gym, int(totalPopSize * (gymperc)))

# Create the population from the subgroups
population = np.append(uofm_students, students_at_gym)

# Set up the figure for plotting
plt.figure(figsize=(10, 12))

# Plot the UofM students only
plt.subplot(3, 1, 1)
sns.distplot(uofm_students)
plt.title("UofM Students Only")
plt.xlim([140, 200])

# Plot the Gym Goers only
plt.subplot(3, 1, 2)
sns.distplot(students_at_gym)
plt.title("Gym Goers Only")
plt.xlim([140, 200])

# Plot both groups together
plt.subplot(3, 1, 3)
sns.distplot(population)
plt.title("Full Population of UofM Students")
plt.axvline(x=np.mean(population))
plt.xlim([140, 200])

plt.show()



'''
In practice !!!!!!!!!!!!!!!!!!!!!!!!!!!!!
What Happens if We Sample from the Entire Population?
We will sample randomly from all students at the University of Michigan.
'''
# Simulation parameters
numberSamps = 5000
sampSize = 50

# Get the sampling distribution of the mean from only the gym
mean_distribution = np.empty(numberSamps)
for i in range(numberSamps):
    random_students = np.random.choice(population, sampSize)
    mean_distribution[i] = np.mean(random_students)

# Plot the population and the biased sampling distribution
plt.figure(figsize = (10,8))

# Plotting the population again
plt.subplot(2,1,1)
sns.distplot(population)
plt.title("Full Population of UofM Students")
plt.axvline(x = np.mean(population))
plt.xlim([140,200])

# Plotting the sampling distribution
plt.subplot(2,1,2)
sns.distplot(mean_distribution)
plt.title("Sampling Distribution of the Mean Weight of All UofM Students")
plt.axvline(x = np.mean(population))
plt.axvline(x = np.mean(mean_distribution), color = "black")
plt.xlim([140,200])

plt.show()