Image Code Python import numpy as np import matplotlib.pyplot as plt from scipy.stats import norm # Create the figure and axis fig, ax = plt.subplots(figsize=(8,6)) # Generate data for a normal distribution mu = 0 # mean sigma = 1 # standard deviation x = np.linspace(mu - 4*sigma, mu + 4*sigma, 1000) y = norm.pdf(x, mu, sigma) # Plot the normal distribution ax.plot(x, y, label='Normal Distribution', color='blue') # 95% confidence interval ci = 0.95 z_value = norm.ppf((1 + ci) / 2) p_minus = mu - z_value * sigma p_plus = mu + z_value * sigma # Plot the vertical lines for the CI ax.axvline(p_minus, color='green', linestyle='--', label=f'{ci*100}% CI: p-') ax.axvline(p_plus, color='green', linestyle='--', label=f'{ci*100}% CI: p+') # Mark the center (mean) with "P" ax.text(mu, norm.pdf(mu, mu, sigma) + 0.02, 'P', ha='center', fontsize=12, color='black') # Mark the CI endpoints with "p+" and "p-" ax.text(p_plus, norm.pdf(p_plus, mu, sigma) + 0.02, 'p+', ha='center', fontsize=12, color='green') ax.text(p_minus, norm.pdf(p_minus, mu, sigma) + 0.02, 'p-', ha='center', fontsize=12, color='green') # Label p-hat near the confidence interval edges p_hat = (p_plus + p_minus) / 2 ax.text(p_hat, norm.pdf(p_hat, mu, sigma) - 0.02, r'$\hat{p}$', ha='center', fontsize=12, color='red') # Add labels and title ax.set_title('Normal Distribution with 95% Confidence Interval', fontsize=14) ax.set_xlabel('Value', fontsize=12) ax.set_ylabel('Probability Density', fontsize=12) # Show the plot plt.legend() plt.grid(True) plt.show() Output
