Chapter 4: The Binomial Probability Distribution
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The Binomial Probability Distribution

An experiment has a binomial probability distribution if three conditions are satisfied.

a. There are a fixed number of trials. The number of trials is denoted by n.

b. The trials are independent.

c. The only outcomes of this experiment can be classified as "succeed" or "fail" (equivalently "yes" or "no"). Furthermore, the probability of success is fixed. The probability of success is denoted by p.

example: A multiple choice test contains 20 questions. Each question has five choices for the correct answer. Only one of the choices is correct. With random guessing, does the test have a binomial probability distribution?

 

 

 

example: An experiment consists of flipping a fair coin 8 times and counting the number of tails. Does this experiment have a binomial probability distribution?

 

 

 

 

example: A pair of dice is rolled 37 times and the number of times a sum of 7 is observed is recorded. Does this experiment have a binomial probability distribution?

 

 

 

example: A multiple choice test contains 20 questions. Each question has four or five choices for the correct answer. Only one of the choices is correct. With random guessing, does this test have a binomial probability distribution?

 

 

 

The probability of exactly x successes in a binomial probability distribution is

binomial_formula.jpg (1725 bytes)

 

example: An experiment consists of flipping a fair coin 8 times and counting the number of tails. Find the probability of seeing exactly 3 tails.

example: A multiple choice test contains 20 questions. Each question has five choices for the correct answer. Only one of the choices is correct. What is the probability of making an 80 with random guessing?

 

 

example: An experiment consists of flipping a fair coin 8 times and counting the number of tails. Find the probability of seeing exactly 6 or 7 tails.

These are mutually exclusive events and thus,

P(x = 6 or x = 7) = .

 

Homework

Section 4-3:  1-3, 5-8, 17-20, 25-27, 29, 31, 33

 

The mean and standard deviation for

a binomial probability distribution

In a binomial probability distribution, the mean and .

 

 

example: An experiment consists of flipping a fair coin 10 times and counting the number of heads. Find the mean and standard deviation for this experiment.

 

 

Approximately 15% of all KSU students commute more than 20 miles one-way to campus.  Would it be unusual in a class of 60 students to have 16 students who commute more than 20 miles one-way to campus?

The mean is 60*.15 = 9 and the standard deviation

.  

Hence the z-score is

and yes, it would be unusual.

 

 

At the KSU library, approximately % of books are returned late.  In the next 1000 books that are returned, would it be unusual to see no late books?

 

 

 

 

Homework

Section 4-4:  1-6, 8, 11, 12

 
Syllabus Files ] Tips for Success ] Intro ] Chapter 2: Numerical Methods ] Chapter 3: Probability ] Chapter 4: Probability Distributions ] Chapter 5: The Normal Curve ] Chapter 5: Central Limit Theorem ] [ Chapter 4: The Binomial Probability Distribution ] Questionnaire ] Chapter 1 ] Chapter 6: Confidence Intervals ] Chapter 6: Required Sample Size ] Chapter 6: Estimation of Proportion ] Required Sample Size (Updated) ] Chapter 7: Hypothesis Testing ] Chapter 7: Applications of Hypothesis Testing ] Sample Tests ]