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

Define the z-values

z_values = [0.29, -1.5, 1.5, -2.35, -3.35]

Calculate areas using the cumulative distribution function (CDF) of the standard normal distribution

area_right_0_29 = 1 - stats.norm.cdf(0.29) area_left_0_29 = stats.norm.cdf(0.29) area_between_neg1_5_1_5 = stats.norm.cdf(1.5) - stats.norm.cdf(-1.5) area_right_neg2_35 = 1 - stats.norm.cdf(-2.35) area_left_neg3_35 = stats.norm.cdf(-3.35)

Values for plotting the standard normal distribution

x = np.linspace(-4, 4, 500) y = stats.norm.pdf(x)

Plot the graph

plt.figure(figsize=(12, 6)) plt.plot(x, y, label='Standard Normal Distribution', color='blue') plt.fill_between(x, 0, y, where=(x >= 0.29), color='red', alpha=0.3, label='Area to Right of z=0.29') plt.fill_between(x, 0, y, where=(x <= 0.29), color='green', alpha=0.3, label='Area to Left of z=0.29') plt.fill_between(x, 0, y, where=(x >= -1.5) & (x <= 1.5), color='yellow', alpha=0.3, label='Area Between z=-1.5 and z=1.5') plt.fill_between(x, 0, y, where=(x >= -2.35), color='purple', alpha=0.3, label='Area to Right of z=-2.35') plt.fill_between(x, 0, y, where=(x <= -3.35), color='orange', alpha=0.3, label='Area to Left of z=-3.35')

Add labels and legend

plt.title('Standard Normal Distribution with Highlighted Areas') plt.xlabel('Z-value') plt.ylabel('Probability Density') plt.legend() plt.grid()

Display the graph

plt.show()

Presenting the calculated areas

results = { "Area to the right of z=0.29": area_right_0_29, "Area to the left of z=0.29": area_left_0_29, "Area between z=-1.5 and z=1.5": area_between_neg1_5_1_5, "Area to the right of z=-2.35": area_right_neg2_35, "Area to the left of z=-3.35": area_left_neg3_35 }

import pandas as pd results_df = pd.DataFrame(list(results.items()), columns=["Scenario", "Area"]) import ace_tools as tools; tools.display_dataframe_to_user(name="Standard Normal Distribution Areas", dataframe=results_df) <<ImageDisplayed>> Scenario Area 0 Area to the right of z=0.29 0.385908 1 Area to the left of z=0.29 0.614092 2 Area between z=-1.5 and z=1.5 0.866386 3 Area to the right of z=-2.35 0.990613 4 Area to the left of z=-3.35 0.000404 Scenario Area 0 Area to the right of z=0.29 0.385908 1 Area to the left of z=0.29 0.614092 2 Area between z=-1.5 and z=1.5 0.866386 3 Area to the right of z=-2.35 0.990613 4 Area to the left of z=-3.35 0.000404successThe calculations for the areas under the standard normal distribution curve are presented in the table displayed. The graph highlights the respective regions for each scenario.

Would you like a detailed explanation of any of these areas or concepts?

Here are five related questions to explore further:

1. What is the significance of the standard normal distribution in statistics?
2. How are z-scores calculated and interpreted in different contexts?
3. What are some real-world applications of finding areas under the standard normal curve?
4. How do cumulative distribution functions (CDFs) relate to the areas under the curve?
5. Can we use these concepts for hypothesis testing and confidence intervals?

Tip: Always ensure that the z-scores are accurate and the corresponding areas match the desired regions for proper analysis.