`# import the important packages

import pandas as pd # library used for data manipulation and analysis

import numpy as np # library used for working with arrays

import matplotlib.pyplot as plt # library for plots and visualizations

import seaborn as sns # library for visualizations

%matplotlib inline

import scipy.stats as stats # this library contains a large number of probability distributions as well as a growing library of statistical functions

# ZED score comparison

# The Z-score formula is:

# Z = (X - μ) / σ

# Where:

# Z is the Z-score

# X is the individual data point

# μ is the population mean

# σ is the population standard deviation

x_1 = 83000

mu_1 = 77000

sigma_1 = 1100

z_1 = (x_1 - mu_1) / sigma_1

print("The Z-score is:", z_1)

x_2 = 92000

mu_2 = 59000

sigma_2 = 1300

z_2 = (x_2 - mu_2) / sigma_2

print("The Z-score is:", z_2)

Formula_A = stats.norm.cdf(z_1) - stats.norm.cdf(z_2)

print (Formula_A)

Formula_B = stats.norm.cdf(x_1,loc=mu_1,scale=sigma_1) - stats.norm.cdf(x_2,loc=mu_2,scale=sigma_2)

print (Formula_B)

`

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