student distribution option

normdist.py

@@ -2,19 +2,22 @@
 # From https://www.geeksforgeeks.org/python/how-to-plot-a-normal-distribution-with-matplotlib-in-python/
 import numpy as np
 import matplotlib.pyplot as plt
-from scipy.stats import norm
+import scipy.stats
 
 data = np.array([1, 1.1, 0.9, 1, 1, 0.9, 0.9])
 lowerbound = 0.9
 upperbound = 1.0
 
 mean = data.mean()
-stddev = data.std()
+stddev = data.std(ddof=1)
+# Delta Degrees of Freedom: ddof=0 for population, ddof=1 for sample std dev
 x = np.linspace(mean-3*stddev, mean+3*stddev, 1000)
-y = norm.pdf(x, mean, stddev)
+y = scipy.stats.norm.pdf(x, mean, stddev)
 plt.plot(x, y, 'b-', label='Normal Distribution')
+#yt = scipy.stats.t.pdf(x, len(data)-1, mean, stddev)
+#plt.plot(x, yt, 'g-', label='T Distribution')
 coloredregion = (x >= lowerbound) & ( x <= upperbound ) #select x values
-plt.vlines([lowerbound, upperbound], 0, plt.ylim()[1])#ylim returns [bot, top]
+plt.vlines([lowerbound, upperbound], 0, plt.ylim()[1], color="red")#ylim returns [bot, top]
 
 plt.fill_between(x, 0, y, where=coloredregion, color="grey", alpha=0.5, label="Design Range")
 plt.xlabel('X')