1 \(Normal(\mu=0, \sigma=1)\) Distribution

1.1 Cumulative Distribution

Here we consider a random variable, Z, with a \(Normal(\mu=0, \sigma=1)\) distribution. This is the Standard Normal distribution. The table below shows the cumulative distribution function \(P(z\leq z)\) and \(P(Z > z)\)

Cumulative Distribution Function (CDF) for a Normal(mu=0, sigma=1) Distribution
z	cdf	one.minus.cdf
-3.00	0.001	0.999
-2.00	0.023	0.977
-1.96	0.025	0.975
-1.64	0.051	0.949
-1.50	0.067	0.933
-1.00	0.159	0.841
-0.75	0.227	0.773
0.00	0.500	0.500
0.75	0.773	0.227
1.00	0.841	0.159
1.50	0.933	0.067
1.64	0.949	0.051
1.96	0.975	0.025
2.00	0.977	0.023
3.00	0.999	0.001

1.1.1 Graphs

Density of Standard Normal Distribution

2 \(Normal(\mu=3, \sigma=1)\) Distribution

2.1 Cumulative Distribution

Here we consider a random variable, Z, with a \(Normal(\mu=3, \sigma=1)\) distribution. The table below shows the cumulative distribution function \(P(X\leq x)\)

Cumulative Distribution for a Normal(mu=3, sigma=1) Distribution
x	cdf	one.minus.cdf
0.00	0.001	0.999
1.00	0.023	0.977
1.04	0.025	0.975
1.36	0.051	0.949
1.50	0.067	0.933
2.00	0.159	0.841
2.25	0.227	0.773
3.00	0.500	0.500
3.75	0.773	0.227
4.00	0.841	0.159
4.50	0.933	0.067
4.64	0.949	0.051
4.96	0.975	0.025
5.00	0.977	0.023
6.00	0.999	0.001

2.1.1 Graphs

Density of Normal(3, sd=1)

3 \(Normal(\mu=3, \sigma=2)\) Distribution

3.1 Cumulative Distribution

Here we consider a random variable, Z, with a \(Normal(\mu=3, \sigma=2)\) distribution. The table below shows the cumulative distribution function \(P(X\leq x)\)

Cumulative Distribution for a Normal(mu=3, sigma=2) Distribution
x	cdf	one.minus.cdf
-3.00	0.001	0.999
-1.00	0.023	0.977
-0.92	0.025	0.975
-0.28	0.051	0.949
0.00	0.067	0.933
1.00	0.159	0.841
1.50	0.227	0.773
3.00	0.500	0.500
4.50	0.773	0.227
5.00	0.841	0.159
6.00	0.933	0.067
6.28	0.949	0.051
6.92	0.975	0.025
7.00	0.977	0.023
9.00	0.999	0.001

3.1.1 Graphs

Density of Normal(3,sd=2)

4 All Graphs

Combined Plots

In Class Exercise: Normal Distributions

putt

12/1/2018