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Appendix B: Computer Resources 355
EXAMPLE B.10
Let a random variable be distributed as normal with mean m = 6 and standard deviation
s = 4. Determine the probability P(8.0 X 14.0).
Solution:
In order to determine the probability P(8.0 X 14.0) we have to first find the probabilities
P(X 8.0) and P(X 14.0). Then P(8.0 X 14.0) = P(X 14.0) – P(X 8.0). Thus, to find
probabilities P(X 8.0) and P(X 14.0) using Minitab we proceed as follows:
1. Enter the test values of 8 and 14 in column C1.
2. From the menu bar select Calc > Probability Distribution > Normal.
3. In the dialog box that appears click on the circle next to Cumulative Probability.
4. Enter 6 (the value of the mean) in the box next to Mean and 4 (the value of the
standard deviation) in the box next to Standard Deviation.
5. Click on the circle next to Input Column and type C1 in the box next to it.
6. Click OK.
7. In the Session window, text will appear as follows, indicating values of
P(X 14.0) = 0.977250 and P(X 8.0) = 0.691462. Thus, P(8.0 X 14.0)
= P(X 14.0) – P(X 8.0) = 0.977250 – 0.691462 = 0.285788.
Normal with mean = 6 and standard deviation = 4
x P(X x)
8 0.691462
14 0.977250
box entitled Normal Distribution to appear. In this dialog box, click on one of
the options available, which are Probability Density, Cumulative Probability,
and Inverse Cumulative Probability. Then enter the value of the Mean and the
Standard Deviation to define the normal distribution. Check the circle next to
Input Column (if you have more than one value of x that you must enter in one
of the data columns, say C1), and enter C1 in the box next to it. Or select Input
Constant Field if you have only one value of x, and enter the value of that constant
in the box next to it. If desired, in the Optional Storage field enter the column in
which you want to store the output. Then click OK.
Shewhart X – and R Control Chart. First enter the data in one column of the
Worksheet window. Then from the command menu select Stat > Control Charts
> Variable Charts for Subgroups > Xbar-R. The dialog box entitled Xbar-R Chart
shown in Figure B.14 appears immediately. We illustrate the construction of an
X – and R chart with the following example.