Minitab Quick Reference
MINITAB GUIDE/MANUAL for Binomial Distribution & Normal Distribution
Minitab Commands for BINOMIAL DISTRIBUTION
To illustrate the commands, consider the following example …
Example: X is a binomial RV with n=20 and p=0.4
a. Find P(X=8)
a.
b. Find P(X<=8)
c. Find P(X>=10)
d. Find P(7<=X<=13)
Click on Calc >> Probability Distributions >> Binomial
*Probability
number of trials 20
probability of success 0.4
*Input Constant 8
Minitab Output P(X=8) = 0.179706
b.
Click on Calc >> Probability Distributions >> Binomial
*Cumulative probability
number of trials 20
Probability of success 0.4
*Input Constant 8
Minitab Output P(X<=8) = 0.595599
c.
Click on Calc >> Probability Distributions >> Binomial
*Cumulative Probability
number of trials 20
probability of success 0.4
*Input Constant 9
Minitab Output P(X<=9) = 0.755337
d.
So, P(X>=10) = 1- 0.755337 = 0.244663
Click on Calc >> Probability Distributions >> Binomial
*Cumulative Probability
number of trials 20
probability of success 0.4
*Input Constant 6
Click on Calc >> Probability Distributions >> Binomial
*Cumulative Probability
number of trials 20
probability of success 0.4
*Input Constant 13
Minitab Output P(X<=6) = 0.250011 P(X<=13) = 0.993534 giving P(7<=X<=13) = 0.993534-0.250011 = 0.743523
Using Minitab to find Normal probabilities (Skill #1) and to find values of the Normal RV (skill #2).
Skill #1 Finding Normal probabilities (When X is Normal with mean = mu and stdev =sigma)
Click on Calc >> Probability Distributions >> Normal
*Cumulative Probability
Mean mu
Standard deviation sigma
*Input Constant k
Whatever value of k you input Minitab gives P (X<=k)
(When X is Normal with mean = mu and stdev =sigma)
Skill#2 Finding values of X (When X is Normal with mean = mu and stdev =sigma)
Click on Calc >> Probability Distributions >> Normal
*Inverse cumulative probability
Mean mu
Standard deviation sigma
*Input constant p
p must be a value between 0 and 1
Whatever value of p you input Minitab gives # so that P(X<=#) = p
Minitab Binomial Capabilities
Choose Calc > Probability Distributions > Binomial
Consider X distributed Binomial n,p to find
P(X = x)
Enter the value of n
Enter the value of p
Enter the value of x
Consider X distributed Binomial n,p to find
P(X <= x)
Enter the value of n
Enter the value of p
Enter the value of x
Minitab Normal Capabilities
Choose Calc > Probability Distributions > Normal
Consider X distributed
Normal mean μ and stdev σ to find
P(X <= x)
Enter the value of μ
Enter the value of σ
Enter the value of x
Consider X distributed
Normal mean μ and stdev σ to find
the value of x such that P(X <= x) = p
Enter the value of μ
Enter the value of σ
Enter the value of p
MINITAB has recently added other way/feature for working with distributions …
Finding Values for Theoretical Distributions
To find a probability or a percentile from a theoretical distribution, go to:
Graph => Probability Distribution Plot => Select “View Probability” and click OK.
You will see the “Distribution” screen, and can select Normal, Binomial, t, or other distributions
off the drop-down menu, and enter any relevant parameters (such as n, p for the Binomial).
You should then select the “Shaded Area” tab.
You can opt to put in a Probability (area) or an X-value (cutoff or boundary value),
and you can select Left tail, Right tail, or Two-tail or Middle.
Make the selections and click OK and you will see the result.
Example – consider a Normal Model with mean 100 and stdev = 15
To find the probability less than 120 …
Example – consider a Normal Model with mean 100 and stdev = 15
To find the 77th percentile …
Distribution Plot
Normal, Mean=1 00, StDev=1 5
0.030
0.025
Density
0.020
0.01 5
0.77
0.01 0
0.005
0.000
100
X
111.1
Example – consider a Binomial Model with n = 80and p = 0.4
To find P(X <= 30)
Distribution Plot
Binomial, n=80, p=0.4
0.09
0.08
Probability
0.07
0.06
0.05
0.04
0.03
0.3687
0.02
0.01
0.00
30
X
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