# 3.2.3 - Minitab: Binomial Distributions

3.2.3 - Minitab: Binomial Distributions##
Minitab^{®}
– Finding Binomial Probabilities using Minitab

Letβs walk through how to calculate the probability of 1 out of 3 crimes being solved in the FBI Crime Survey example.

Recall in that example, \(n=3\), \(p=0.2\).

Using Minitab, calculate \(P(X=1)\):

- From the Minitab menu select
**Calc****>****Probability Distributions****>****Binomial** - A dialog box (below) will appear. Enter 3 into the
**Number of Trials**box and 0.2 into the**Event Probability**box. - Choose
.**Probability** - Choose the
**Input Constant Box**and enter 1. - Choose
.**OK**

The result should be the same probability of 0.384 we found by hand.

Suppose we want to find \(P(X\le 2)\). We can use Minitab to find this cumulative probability.

- From the Minitab menu select
**Calc****>****Probability Distributions****>****Binomial** - Enter in 3 and 0.2 as above.
- Choose
.**Cumulative Probability** - Choose
**Input Constant**and enter 2. - Choose
.**OK**

The result should be \(P(X\le 2)=0.992\).

**Note!**While using Minitab is quicker, you may be expected to compute these probabilities by hand on assignments.

## Note!

Depending on if you have the desktop version or cloud version of MINITAB, you will find minor differences in the order of the steps.

#### Binomial with Minitab

Suppose X follows a binomial distribution with π=3 and π=0.2. Calculate π(π=1).

>**Calc**>**Probability Distributions**. Fill the dialog box as shown below.**Probability Density**##### Binomial with n= 3 and p = 0.2

x

P(X=x)

1

0.383

Suppose X follows a binomial distribution with π=3 and π=0.2. Calculate P(πβ€2).

>**Calc**>**Probability Distributions**. Fill the dialog box as shown below.**Cumulative Distribution Function**

##### Binomial with n= 3 and p = 0.2

x

P(Xβ€x)

2

0.992