Updated the tutorial for reddit post

Author: mGalarnyk

.DS_Store

@@ -4,28 +4,35 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Graph Probability Density Function"
+    "![](images/68_95_99_rule.png)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Probability Density Functions (PDF) do NOT show you the probability of events but their probability density. This notebook will show you how you can use the PDF to find the probability for a given <b>range</b> of numbers. This is basically an explanation of why the graph below makes sense. "
+    "Most people commonly associate the normal distribution with the 68-95-99.7 rule which you can see in the image above. 68% of the data is within 1 standard deviation (σ) of the mean (μ), 95% of the data is within 2 standard deviations (σ) of the mean (μ), and 99.7% of the data is within 3 standard deviations (σ) of the mean (μ)."
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "![](images/NormalDistribution.png)"
+    "This notebook explains how those numbers were derived in the hope that they can be more interpretable for your future endeavors."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Graph Probability Density Function"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The probability density function of a normal distribution with a mean (insert mean symbol) and variance (insert variance symbol) is: (INSERT EQUATION HERE)"
+    "Probability Density Functions (PDF) do NOT show you the probability of events but their probability density. This notebook will show you how you can use the PDF to find the probability for a given <b>range</b> of numbers. This is basically an explanation of why the graph below makes sense. "
    ]
   },
   {
@@ -45,7 +52,6 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "import scipy.integrate as integrate\n",
     "import scipy.special as special\n",
     "from scipy.integrate import quad\n",
     "import numpy as np\n",
@@ -1260,6 +1266,34 @@
     "\n",
     "fig.savefig('images/68_95_99_rule.png', dpi = 1200)"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Breaking it Down Further"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "You can further break it down "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "![](images/NormalDistribution.png)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {

Statistics/.DS_Store

@@ -4,28 +4,35 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Graph Probability Density Function"
+    "![](images/68_95_99_rule.png)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Probability Density Functions (PDF) do NOT show you the probability of events but their probability density. This notebook will show you how you can use the PDF to find the probability for a given <b>range</b> of numbers. This is basically an explanation of why the graph below makes sense. "
+    "Most people commonly associate the normal distribution with the 68-95-99.7 rule which you can see in the image above. 68% of the data is within 1 standard deviation (σ) of the mean (μ), 95% of the data is within 2 standard deviations (σ) of the mean (μ), and 99.7% of the data is within 3 standard deviations (σ) of the mean (μ)."
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "![](images/NormalDistribution.png)"
+    "This notebook explains how those numbers were derived in the hope that they can be more interpretable for your future endeavors."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Graph Probability Density Function"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The probability density function of a normal distribution with a mean (insert mean symbol) and variance (insert variance symbol) is: (INSERT EQUATION HERE)"
+    "Probability Density Functions (PDF) do NOT show you the probability of events but their probability density. This notebook will show you how you can use the PDF to find the probability for a given <b>range</b> of numbers. This is basically an explanation of why the graph below makes sense. "
    ]
   },
   {
@@ -45,7 +52,6 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "import scipy.integrate as integrate\n",
     "import scipy.special as special\n",
     "from scipy.integrate import quad\n",
     "import numpy as np\n",
@@ -1260,6 +1266,34 @@
     "\n",
     "fig.savefig('images/68_95_99_rule.png', dpi = 1200)"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Breaking it Down Further"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "You can further break it down "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "![](images/NormalDistribution.png)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {