Mon, 3/17, 4.3, MAT123, Spring 2025

MAT123 Spring 2025 Notes

Mon, 3/17, 4.3

4.3 Binomial Distribution: a) Identify the characteristics of binomial experiment; b) Use the Binomial distribution to solve applied probability problems; c) Use software to construct a bar chart for probabilities of a Binomial random variable (Lab 5) 7

To be BINOMIAL:

There are n, a specific number, of trials -- n identical actions.
Each trial is independent -- the result of one trial has no effect on another trial.
Each trial has only 2 outcomes -- success or failure.
The probabililty of success on a trail is called p. P(success) = p.
The probabililty of failure on a trail is called q. P(failure) = q.
This also means that q = 1 - p and p = 1 - q.
The number of successes in the n trials is the variable.
The probability of x successes in n independent trials is given by the formula:
The mean and standard deviation of a binomial distribution are stated below.

A Binomial Distribution Presents An Action with Only Two Possible Outcomes
Binomial in algebra means the sum of two terms.
: as in the above binomial expansions with Pascal's Triangle highlighted in blue.

Note: The blue coefficients above match the frequencies below.

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