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Binomial Distributions

In some probability experiments, there are exactly two possible outcomes. For example:

• When flipping a coin, you get heads or tails. When flipping a coin 200 times, what is the probability of getting heads exactly 101 times? (The answer is 5.58 percent)

In some probability experiments, there are exactly two possible outcomes. For example:

• When answering a question on a multiple choice test, your answer will be right or wrong. What is the probability of getting 50 percent of the answers correct if there are four choices for each question, and you guess each answer?

• When flipping a coin, you get heads or tails. When flipping a coin 200 times, what is the probability of getting heads exactly 101 times? (The answer is 5.58 percent)

In some probability experiments, there are exactly two possible outcomes. For example:

• When a manufacturer guarantees a toaster for one year, the toaster will work fine or fail in one year. The manufacturer knows that, on average, 5 percent of the toasters fail. What is the probability that the manufacturer will have to replace 120 or more toasters in a year when 2000 toasters are sold?

• When answering a question on a multiple choice test, your answer will be right or wrong. What is the probability of getting 50 percent of the answers correct if there are four choices for each question, and you guess each answer?

• When flipping a coin, you get heads or tails. When flipping a coin 200 times, what is the probability of getting heads exactly 101 times? (The answer is 5.58 percent)

In some probability experiments, there are exactly two possible outcomes. For example:

• When a manufacturer guarantees a toaster for one year, the toaster will work fine or fail in one year. The manufacturer knows that, on average, 5 percent of the toasters fail. What is the probability that the manufacturer will have to replace 120 or more toasters in a year when 2000 toasters are sold?

• When answering a question on a multiple choice test, your answer will be right or wrong. What is the probability of getting 50 percent of the answers correct if there are four choices for each question, and you guess each answer?

• When flipping a coin, you get heads or tails. When flipping a coin 200 times, what is the probability of getting heads exactly 101 times? (The answer is 5.58 percent)

Binomial Distributions

Type of Distributions...

Example: graph the distribution that shows what can happen when a 6-sided die is thrown.

Uniform Distribution: data may be discrete or continous. Every outcome in the experiment is equally likely.

Uniform (Probability) Distribution

Probabilities of outcomes when rolling a six sided die.

No data between 0 and 1.

Type of Distributions...

Normal Distributions: Data is continous (height, weight, time, etc.) when certain experiments are carried out many, many, many times the probability graph of the data tend to be "bell shaped" this is known as the Normal Curve.

Type of Distributions...

Binomial Distribution: data is discrete (# of heads when ten coins are tossed, # of spades in a 13 card hand , etc.). When a binomial experiment is conducted many, many, many times a portion of the related histogram approaches the shape of the normal curve.

Experimental Binomial (Probability) Distribution

Theoretical Binomial (Probability) Distribution

Probability of the number of girls in a family of four.

Experimental Binomial (Probability) Distributiontake

note

Theoretical Binomial (Probability) Distributionbinompdf(trials, p, x [this is optional])

trials = number of trials p = P(success) x = specific outcome

• When a manufacturer guarantees a toaster for one year, the toaster will work fine or fail in one year. The manufacturer knows that, on average, 5 percent of the toasters fail. What is the probability that the manufacturer will have to replace 120 or more toasters in a year when 2000 toasters are sold?

binompdf(trials, p, x [this is optional]) trials = number of trials p = P(success) x = specific outcome

The Binomial Coin Experiment

http://www.math.uah.edu/stat/applets/BinomialCoinExperiment.xhtml