Plot the following function. This is the pdf for a standard normal random variable.
1
fZ ( z) e 0.5 z z
2
2
z pdf Standard Normal PDF
-5
-4.9 1.2
-4.8
-4.7 1
-4.6
-4.5 0.8
-4.4
-4.3 0.6
-4.2
-4.1 0.4
-4
-3.9 0.2
-3.8
-3.7
0
-3.6
-3.5 -6 -4 -2 0 2 4 6
-3.4
-3.3
-3.2
-3.1
-3
-2.9
-2.8
-2.7
-2.6
-2.5
-2.4
-2.3
-2.2
-2.1
-2
-1.9
-1.8
-1.7
-1.6
-1.5
-1.4
-1.3
-1.2
-1.1
-1
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
5
Use NORMDIST to generate values of the pdf and cdf for Z . Note: There are several commands that
could be used, but NORMDIST can be used in a wide variety of situations.
What does your knowledge of calculus tell you about these two graphs?
z pdf cdf
-5
Standard Normal PDF
1.2
-4.9
-4.8 1
-4.7
-4.6 0.8
-4.5
0.6
-4.4
-4.3 0.4
-4.2
-4.1 0.2
-4 0
-3.9
-5 -3 -1 1 3 5
-3.8
-3.7
-3.6 Standard Normal CDF
1.2
-3.5
-3.4 1
-3.3
-3.2 0.8
-3.1 0.6
-3
-2.9 0.4
-2.8
0.2
-2.7
-2.6 0
-2.5 -5 -3 -1 1 3 5
-2.4
-2.3
-2.2
-2.1
-2
-1.9
-1.8
-1.7
-1.6
-1.5
-1.4
-1.3
-1.2
-1.1
-1
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4.0
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
5.0
Use NORMDIST to plot pdfs of two non-standard nomral random variables. How does the value of the
mean and standard deviation affect the graphs?
x
2
0.5
Note: The general formula for the pdf is f X ( x)
1
e x
2
2, 1 0, 0.5
x pdf pdf 1.2
-5
-4.9 1 N (0, 0.5)
-4.8
0.8
-4.7
-4.6
0.6
-4.5
-4.4
0.4
-4.3
-4.2 N (2,1)
0.2
-4.1
-4 0
-3.9
-4 -3 -2 -1 0 1 2 3 4 5 6
-3.8
-3.7
-3.6
-3.5
-3.4
-3.3
-3.2
-3.1
-3
-2.9
-2.8
-2.7
-2.6
-2.5
-2.4
-2.3
-2.2
-2.1
-2
-1.9
-1.8
-1.7
-1.6
-1.5
-1.4
-1.3
-1.2
-1.1
-1
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
5
Let X be a normal random variable with mean 35 and variance 25. Let Z be the standard normal rv.
Use NORMDIST and NORMINV to find the following:
1. Find P ( X 40)
2. Find P ( Z 1.2)
3. Find P( Z )
4. Find the value of b so that P(Z b) 0.6
5. Find the value of b so that P(b Z b) 0.96
Example: Use the standard normal random variable to find the probability
P ( X 10) where X N (7,3)
X 7 10 7
P ( X 10) P
3 3
P ( Z 1)
0.841345
1) Use the standard normal random variable to find
P(20 Y 50) where Y N (40,18)
2) Use the standard normal random variable to find b so that
P(b T b) 0.95 where T N (0, 4.6)