The Binomial Distribution Worksheet

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4.3 The Binomial Distribution
Key concepts: Binomial experiment, success, failure, number of successes, binomial
distribution
Characteristics of a Binomial Experiment
1. The experiment consists of n identical trials (repetitions).
2. There are only two possible outcomes on each trial. We will denote one
outcome by S (for success) and the other by F (for failure).
3. The probability of S remains the same from trial to trial. This probability is
denoted by p, and the probability of F is denoted by q. Note that q = 1 − p.
4. The trials are independent.
x
5. The binomial random variable
is the number of successes S in n trials
Examples:
 Rolling a die 10 times and counting number of times it turns “six”, success = six, p = 1/6, q = 5/6, n =
10
 Taking multiple choice (choice A-E) exam completely unprepared, x = number of correct answers,
success = correct answer, p = 1/5, n = number of questions
 Sampling products coming out of production line, x = number of defective in a sample, success =
defective item, p = proportion of defectives, n = sample size
 Selecting a sample of 100 students at a university and counting graduate students, success = graduate
student, p = proportion of graduate students at the university, n=100
NOTE: If we select a sample without replacement then trials are not independent. But if the population is
more than 10 times the sample, then they are almost independent and we can treat it as a binomial experiment.

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