# Binomial Distribution TI-84 | TI-83

Joestat wants to help you do a Binomial Probability Distribution calculation using your TI-84 or TI-83 to calculate the following examples.

Help is available for the following types of Binomial Probability Distribution problems:
Find the chance of an exact outcome.
Find the probability of a maximum outcome.
Find the percentage of a minimum outcome.

Example 1: Calculate the binomial probability distribution TI-84 or TI-83 given p and q for an exact outcome.

Problem 1: In a school survey 68% of the students have an Android device. What is the probability that 12 of a selecting of 20 have Android devices.

Solution:
n = 20 (20 classmates)
x = 12 (The amount of people who own an android)
p = .68 (probability that they are an Android user is a success, because that is what we care about)
q = .32 (probability that the users does not own an android)
Reminder: Q=1-p and p=1-q thus q=1-.68=.32
The following is how the problem would be solved by hand using the Binomial Distribution Formula. When looking for and exact value use binopdf on your TI-84 and TI-83 calculator.
binompdf(20,.68,12) is approximately .1354

[2ND] | [VARS] |  |  |  | [,] | [.] |  |  | [,] |  | Note: Some TI-84’s use a different OS the Binomial Distribution must be completed as followed:
[2ND] | [VARS] | [ALPHA] | [MATH] |  |  | [ENTER] | [.] |  |  | [ENTER] |  |  | [ENTER] | [ENTER]

Problem 2: What is the probability that out of 14 classmates that exactly 8 use iphones.

Solution:
n = 14
x = 8 (The amount of people who own an iphone
p = .32 (Probability that they are an users is the success, because that is what we care about)
q = .68 (Probability that they do not own an iphone)

When looking for and exact value use binomial pdf on your TI-84 and TI-83 calculator.
bindompdf(14,.32,8) is approximately .0326

[2ND] | [VARS] |  |  |  | [,] | [.] |  |  | [,] |  | [ENTER] Alternate OS:
[2ND] | [VARS] | [ALPHA] | [MATH] |  |  | [ENTER] | [.] |  |  | [ENTER] |  | [ENTER] | [ENTER] | [ENTER]

Example 2: Calculate the binomial probability distribution TI-84 or TI-83 given p for a maximum outcome.

It was found that the Statistics pass rate was 95% for students that use tistats.com. (based on the provided, which may or may not be accurate)

Problem: What is the probability that out of 32 students 26 or less pass.

N = 32
x = 26 (Number of students who passed)
p = .95 (Probability of passing)
q = .05 (Probability of failing)
Note P=1-Q and Q=1-P.
thus 1-.95 = .05 = Q

When finding a ranged of values use the binomcdf function.

[2ND] | [VARS] | [ALPHA] | [MATH] |  |  | [,] | [.] |  |  | [,] |  | Alternate OS: [2ND] | [VARS] | [ALPHA] | [APP] |  |  | [ENTER] | [.] |  |  | [ENTER] |  |  [ENTER] [ENTER] [ENTER]

Extra Credit:

Problem: What is the probability that from our sample of 32 a minimum of 3 students fail.

N = 32
x = 2 (The amount of people we think will fail)
p = .05 (Probability of failing, which is what we want to know about)
q = .95 (Probability of Success)
n=number of trials
x- number of success that happen during n trails
p = Probability of success [Note: If given the q then (p = 1-q)]
q = Probability of failure [Note: If given q then (q=1-p)]

Note: The probability that 3 or more students will fail is the same as 1 – the probability of 2 or less failing. With this fact we can use the binomcdf(n,p,x) to solve the problem.

1-binomcdf(32,.05,2)
 | [-] | [2ND] | [VARS] | [ALPHA] | [MATH] |  |  | [,] | [.] |  |  | [,] | Alternate OS:
 | [-] | [2ND] | [VARS] | [ALPHA] | [APP] |  |  | [ENTER] | [.] |  |  | [ENTER] |  [ENTER] | [ENTER] | [ENTER]