Мат_Стат_Мірошниченко_СР№2.1

import numpy as np
import pandas as pd
import scipy.stats as stats
import matplotlib.pyplot as plt
from IPython.display import Latex

data = [3.31, 1.15, 2.44, 0.82, 1.50, 2.53, 2.18, 3.20,
        2.85, 2.27, 1.97, 0.98, 3.51, 2.42, 2.09, 2.83,
        2.76, 0.18, 1.61, 2.21, 2.33, 3.06, 1.70, 2.44,
        1.82, 3.02, 3.63, 1.52, 2.01, 2.17, 2.63, 1.94,
        2.49, 2.31, 2.37, 1.03, 2.06, 0.67, 2.79, 2.42,
        2.95, 0.45, 1.20, 1.61, 2.35, 1.73, 0.82, 1.10,
        1.94, 2.14, 2.28, 2.54, 1.85, 2.40, 1.94, 1.30,
        1.62, 2.03, 2.00, 2.70, 2.33, 2.86, 3.26, 1.71,
        2.70, 2.96, 2.89, 0.73, 1.01, 1.85, 2.79, 3.10,
        2.42, 3.12, 2.43, 1.85, 1.21, 1.53, 2.95, 1.22]

desc_stats = pd.DataFrame(columns=['Valid N', 'Mean', 'Min', 'Max', 'Std.Dev.', 'Skewness', 'Kurtosis'], index=['Value'])
desc_stats.loc['Value'] = [len(data), np.mean(data), min(data), max(data), np.std(data), stats.skew(data), stats.kurtosis(data)]
print(desc_stats)


counts, bin_edges, _ = plt.hist(data, bins=10, edgecolor='black')
plt.xticks(ticks=bin_edges, rotation=45, ha='right')
plt.title('Гістограма')
plt.xlabel('Інтервали')
plt.ylabel('Частота')
plt.show()

# Розрахунок ймовірності для інтервалу P(1.22 < X < 1.84)
mean = np.mean(data)
std_dev = np.std(data)

# Функція нормального розподілу
prob_1_22 = stats.norm.cdf(1.84, mean, std_dev) - stats.norm.cdf(1.22, mean, std_dev)
display(Latex(f"Ймовірність $P(1.22 < X < 1.84): {round(prob_1_22*100, 2)}$%"))

lower_bound = mean*0.9
upper_bound = mean*1.1

prob_lower = stats.norm.cdf(lower_bound, mean, std_dev)
prob_upper = stats.norm.cdf(upper_bound, mean, std_dev)

probability = prob_upper - prob_lower
percentage = probability * 100

display(Latex(f"Випуск придатної продукції: ${round(percentage, 2)}$%"))