# 3.2.3 - Minitab: Binomial Distributions

3.2.3 - Minitab: Binomial Distributions

## Minitab® – Finding Binomial Probabilities using Minitab

Letβs 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 $$P(X=1)$$:

1. From the Minitab menu select Calc > Probability Distributions > Binomial
2. A dialog box (below) will appear. Enter 3 into the Number of Trials box and 0.2 into the Event Probability box.
3. Choose Probability .
4. Choose the Input Constant Box and enter 1.
5. 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.

1. From the Minitab menu select Calc > Probability Distributions > Binomial
2. Enter in 3 and 0.2 as above.
3. Choose Cumulative Probability .
4. Choose Input Constant and enter 2.
5. 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

1. Suppose X follows a binomial distribution with π=3 and π=0.2. Calculate π(π=1).

Calc > Probability Distributions > Probability Density. Fill the dialog box as shown below.

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

x

P(X=x)

1

0.383

2. Suppose X follows a binomial distribution with π=3 and π=0.2. Calculate P(πβ€2).

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

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

x

P(Xβ€x)

2

0.992

 [1] Link ↥ Has Tooltip/Popover Toggleable Visibility