10000_samples.py

import numpy as np
import seaborn as sns
samples = np.zeros(10000)
mu, sigma = 20, 3
for s in range(10000):
    sample = np.random.normal(mu, sigma, 250)  #sample of size 250
    x_bar = sample.mean()                      #calculating sample mean
    samples[s] = x_bar
sns.distplot(samples, hist = True, color = 'darkblue', 
             hist_kws={'edgecolor':'black'}).set(xlabel = 'Sample Mean', 
                                           ylabel = 'Density')