Eliminated redundant file, and renamed solution S6_3_1_normalDistribution.py

Author: thomas-haslwanter

ISP/Exercise_Solutions/S6_3_1_normalDistribution.py

@@ -1,16 +1,73 @@
-'''Solutions to 6.3.1 Examples of Normal Distributions'''
+"""Solution to the Examples in Section 6.3.1"""
 
-# author: Thomas Haslwanter, date: Oct-2015
+# author:   Thomas Haslwanter
+# date:     Sept-2019
 
-# Import standard packages
+# Import the required packages
 import numpy as np
 from scipy import stats
 
-# Example 1
-nd = stats.norm(175, 6)
-p = nd.cdf(184) - nd.cdf(183)
-print('The probability that a randomly selected man is 183 cm tall is {0:.1f}% .'.format(p*100))
 
-# Example 2
+def man_183():
+    """If cans are assumed to have a standard deviation of 4 g, what does the average
+       weight need to be in order to ensure that 99 % of all cans have a weight of at least
+       250 g?
 
-# Example 3
+       To answer that question, we calculate the probability that the size is
+       between 183.0 and 184.0 cm."""
+    
+    # Define the distribution
+    mean = 175
+    sd = 6
+    nd = stats.norm(mean, sd)
+    
+    # Calculate and show the probability
+    prob_183 = 100*(nd.cdf(184) - nd.cdf(183))
+    print(f'The probability that a man is exactly 183 cm tall is {prob_183:4.1f} %')
+    
+    # Note that here I use "f-strings", which only have become available in Python 3.7.
+    # For Python 3.6 or earlier, you have to use:
+    # print('The probability that a man is exactly 183 cm tall is {0:4.1f} %'.format(prob_183))
+    
+
+def weight_cans():
+    """If cans are assumed to have a standard deviation of 4 g, what does the average
+    weight need to be in order to ensure that 99 % of all cans have a weight of at least
+    250 g? """
+    
+    # Define the parameters
+    sd = 4
+    lower_lim = 250
+    nd = stats.norm()
+    
+    # Calculate the average weight, and show the result
+    mean = lower_lim + sd * nd.ppf(0.99)
+    print(f'If the average can weighs {mean:4.1f} g and the standard ' + 
+          f'deviation is {sd} g, then 99% will weigh above {lower_lim} g.')
+    
+    
+def small_men():
+    """ If cans are assumed to have a standard deviation of 4 g, what does the average
+    weight need to be in order to ensure that 99 % of all cans have a weight of at least
+    250 g?
+    """
+    
+    # Define the parameters
+    male = {'avg':175, 'sd':6}
+    female = {'avg':168, 'sd':3}
+    
+    # Calculate the distribution for the difference between a randomly selected man, and a randomly selected woman
+    diff = {'avg':male['avg'] - female['avg'], 'sd': np.sqrt(male['sd']**2 + female['sd']**2)}
+    nd = stats.norm(diff['avg'], diff['sd'])
+    p_small_male = nd.cdf(0)
+    
+    # Show the likelyhood that the man is smaller
+    print(f'The probability that a randomly selected man is shorter than a randomly selected woman is {p_small_male*100:4.1f}%.')
+    
+    
+if __name__ == '__main__':
+    """Run the individual solutions"""
+    man_183()
+    weight_cans()
+    small_men()
+