# UTPA STEM/CBI Courses/Probability and Statistics/Binomial Distribution (Anahit Galstyan)

Course Title: Precalculus and Trigonometry
Lecture Topic: Probability and Statistics
Instructor: Anahit Galstyan
Institution:University of Texas-Pan American

## Backwards Design

Course Objectives
* Primary Objectives- By the next class period students will be able to:
** Find probabilities of events related to binomial random variables
** Use the binomial probability tables and the TI 84 calculator to calculate binomial probability
** Analyze, describe and summarize their findings
* Sub Objectives- The objectives will require that students be able to:
** Understand Bernoulli Scheme.
** Understand the relationship between the mean and the binomial parameters.
* Difficulties- Students may have difficulty:
** Setting up the problem.
** Identifying the parameters of the binomial distribution.
* Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
** Finding the probability between failure and success.
** Building models based on binomial distribution.
Model of Knowledge
* Concept Map
** Understand the concept of a random variable.
** Understand the concept of expected value.
** Analyze, describe and summarize the data.
* Content Priorities
** Enduring Understanding
*** Understand the binomial model
*** Understand why to use binomial probability
*** Advantages and disadvantages of using binomial probability
** Important to Do and Know
*** Express probabilities of events in terms of random variables.
*** Know how to use the binomial probability tables.
*** Know how to use the TI 84 to find binomial probabilities.
** Worth Being Familiar with
*** Parameters
*** Binomial distribution formula
*** Mean, Variance and Standard Deviation formulas
Assessment of Learning
* Formative Assessment
** In Class (Groups)
*** Work solving problems
*** Helping each other to solve the review
** Homework (individual)
*** Pre-lecture quiz after student has read the section from the book
*** Recommended problems from the book.
* Summative Assessment
** Tests
** Final Exam

## Legacy Cycle

OBJECTIVE
By the next class period, students will be able to:
* Find probabilities of events related to binomial random variables
* Use the binomial probability tables and the TI 84 calculator to calculate binomial probability
* Analyze, describe and summarize their findings
The objectives will require that students be able to:
* Understand Bernoulli Scheme.
* Understand the relationship between the mean and the binomial parameters.
THE CHALLENGE
65% of the college students who are in a relationship achieve better grades than the college students who are not in a relationship. You randomly select 10 college students and ask each to name if he or she achieve better grades when they are in a relationship. Find the probability that the number of college students who say that when they are in a relationship, they achieve better grades. If convenient, use technology to find the probabilities.
GENERATE IDEAS
We should be in a relationship.
MULTIPLE PERSPECTIVES
We need to know the probability of success.
RESEARCH & REVISE
Students will be able to use their book and calculator. Students will work in groups.
TEST YOUR METTLE
The groups will present their ideas to the class and will receive feedback. Students will take a quiz at the beginning of the following class.
GO PUBLIC
Students will be able to answer similar questions presented at the beginning of the lesson and would be asked to turn in a summary of their findings.

## Pre-Lesson Quiz

* What is a binomial random variable?
* What does the Bernoulli Scheme assume?
* What does μ, n, p, and q represent?
* What are the advantages of using Binomial Probability?
* What are the disadvantages of using Binomial Probability?

## Test Your Mettle Quiz

65% of the college students who are in a relationship achieve better grades than the college students who are not in a relationship. You randomly select 10 college students and ask each to name if he or she achieve better grades when they are in a relationship. Find the probability that the number of college students who say that when they are in a relationship, they achieve better grades. Find the binomial probability of exactly two, more than two and between two and five inclusive. If convenient, use technology to find the probabilities.