13 Example - Analyzing distribution of sum of two normally distributed random variables

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import numpy as np
import pandas as pd
from pandas import Series, DataFrame
import matplotlib.pyplot as plt
import seaborn as sns
from scipy import stats

khanacademy

df = DataFrame({'mean': [10, 10], 'std. dev.': [1.5, 2]}, index=['To work', 'To home'])

df

	mean	std. dev.
To work	10	1.5
To home	10	2.0

mean = df['mean'].sum()

var = (df['std. dev.']**2).sum()

std = np.sqrt(var)

mean, var, std

(20, 6.25, 2.5)

x = 25

z_score = (x - mean) / std

z_score

2.0

stats.norm.cdf(z_score)

0.9772498680518208

# find a way to get the ztable and plot the normal dist