This document discusses using Minitab instead of tables to find probabilities and z-values for the standard normal distribution. It provides examples of finding probabilities for given z-values using both tables and Minitab, and shows that Minitab makes the calculations faster and easier. The document also demonstrates how to use Minitab to find z-values for given probabilities, as well as find the z-values that define a symmetric probability between them. Overall, the document promotes using Minitab over tables for standard normal distribution calculations.

1. USING MINITAB INSTEAD
OF TABLES
Z VALUES, PROBABILITIES,
ETC.
B. Heard
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permission. Students may
download one copy for their
own personal use.

2. USING MINITAB INSTEAD OF
TABLES
First, I will note that learning to use tables in a statistics class is
important.
However, I will also note that if you have access to Minitab, it is much
easier and much less stress on your eyes…
So let’s take a look at some basic questions and approach them with
the table and Minitab to see if we get the same answers.

3. USING MINITAB INSTEAD OF
TABLES
Question: Find the area to the left (probability of being less than) for
a z score of 1.35.

4. USING MINITAB INSTEAD OF
TABLES
As you can see from the table, the answer is 0.9115

5. USING MINITAB INSTEAD OF
TABLES
Not too bad with the table, but take a look at doing this in Minitab…
Go to Graph >> Probability Distribution Plots >> Click View
Probability

6. USING MINITAB INSTEAD OF
TABLES
Make sure the Distribution is set to “Normal” and the Mean is 0 and
the Standard Deviation is 1
The Standard Normal is
simply a Normal
Distribution with a Mean of
0 and Standard Deviation of
1.
There is no “Magic.”
A “z-score” is simply the
number of standard
deviations away from the
mean a value is…

7. USING MINITAB INSTEAD OF
TABLES
Click the Shaded Area Tab…

8. USING MINITAB INSTEAD OF
TABLES
I want to know the probability to the left of a z score of 1.35. The z
score is just the “x value” and I’m looking for the probability.
Click X Value
Click Left Tail
Input 1.35 for X value

9. USING MINITAB INSTEAD OF
TABLES
Are you amazed? No flipping to the table every time you need to
figure it out….
0.4
0.3
0.2
0.1
0.0
X
Density
1.35
0.9115
0
Distribution Plot
Normal, Mean=0, StDev=1

10. USING MINITAB INSTEAD OF
TABLES
Question: Find the area to the right (probability of being greater
than) for a z score of -2.07.

11. USING MINITAB INSTEAD OF
TABLESThe table gives me the area to the left of the z score. The area to the
left is 0.0192, BUT I now have to say 1- 0.092 to get the correct
answer of 0.9808

12. USING MINITAB INSTEAD OF
TABLESMinitab is ready and waiting, same initial steps, but after clicking the
Shaded Area tab
I want to know the probability to the right of a z score of -2.07.
Click X Value
Click Right Tail
Input -2.07 for X value

13. USING MINITAB INSTEAD OF
TABLES
Bazinga, no subtracting from 1, or even worrying about it…
0.4
0.3
0.2
0.1
0.0
X
Density
-2.07
0.9808
0
Distribution Plot
Normal, Mean=0, StDev=1

14. USING MINITAB INSTEAD OF
TABLES
Quizzes are known to include questions like P(-0.31<z<1.38)…
With the tables, you have to find the probability values for both,
subtract the largest from the smallest, etc. etc.
It works great, but leaves room for calculation errors…

15. USING MINITAB INSTEAD OF
TABLESMinitab is ready and waiting, same initial steps, but after clicking the
Shaded Area tab
I want to know the probability between two z values.
Click X Value
Click Middle
Input -0.31for X value 1
Input 1.38 for X value 2

16. USING MINITAB INSTEAD OF
TABLES
Yes, it is that easy… The answer would be 0.5379
0.4
0.3
0.2
0.1
0.0
X
Density
-0.31
0.5379
1.380
Distribution Plot
Normal, Mean=0, StDev=1

17. USING MINITAB INSTEAD OF
TABLES
The other type question they can ask, is something like “Find the z
value with a probability of 0.4483 to the left or a probability of
0.4483 for “less than z”
Same general approach, BUT after clicking the Shaded Area Tab

18. USING MINITAB INSTEAD OF
TABLES
CLICK THE RADIAL BUTTON Next to Probability
Click Left Tail
Enter 0.4483 for the
Probability

19. USING MINITAB INSTEAD OF
TABLES
Round the value to TWO Decimals unless otherwise requested
Answer
A z score of
-0.13
0.4
0.3
0.2
0.1
0.0
X
Density
-0.1300
0.4483
0
Distribution Plot
Normal, Mean=0, StDev=1

20. USING MINITAB INSTEAD OF
TABLES
You can do the same thing for probabilities greater than using a Right
Tail.
There is one other type of question that sometimes throws students
and Minitab makes it incredibly easy…

21. USING MINITAB INSTEAD OF
TABLES
Find the values for +/- z where 75.4%% of the area is distributed
symmetrically between the two values.
They may say word it, “Find +/- z, where 0.7540 = P(-z<x<z)
This one is incredibly easy.

22. USING MINITAB INSTEAD OF
TABLES
Find the values for +/- z where 75.4% of the area is distributed
symmetrically between the two values.
They may say word it, “Find +/- z, where 0.7540 = P(-z<x<z)
Ask yourself how much area is in the tails? (1-0.7540 = 0.2460)
Ok, remember I have 0.2460 TOTAL AREA IN BOTH TAILS

23. USING MINITAB INSTEAD OF
TABLES
CLICK THE RADIAL BUTTON Next to Probability
Click Both Tails
Enter 0.2460 for the
Probability

24. USING MINITAB INSTEAD OF
TABLES
What is my answer? -1.16 and 1.16
0.4
0.3
0.2
0.1
0.0
X
Density
-1.160
0.123
1.160
0.123
0
Distribution Plot
Normal, Mean=0, StDev=1

25. USING MINITAB INSTEAD OF
TABLES
Just read the questions carefully and PRACTICE, PRACTICE, PRACTICE
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