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Binomial Probability Distribution Examples and Formulas

This section explores binomial probability distribution, including formulas, examples, and calculations of probabilities, means, and standard deviations. It covers experiments with two outcomes, fixed number of trials, and independent events. The examples include rolling a die, drawing cards, and administering a drug to individuals.

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Binomial Probability Distribution Examples and Formulas

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  1. Section 6.2 Binomial Probability Distribution Obj: Identify and construct binomial distributions

  2. Binomial Experiments Criteria Are only 2 possible outcomes The experiment has a fixed number of trials – each of which are independent The probability of a success is the same

  3. Binomial? • A single die is rolled 100 times and the outcome is recorded. • Five cards are randomly drawn from a deck of 52 without replacement and the number of aces is recorded. • An experimental drug is administered to 100 randomly selected individuals. The individuals with a favorable reaction was recorded.

  4. Binomial Probability Distribution Formula to find the probability of x successes in n trials of a binomial experiment, where the probability of success is p: Given that 70% of all households have cable, in a sample of 15, what is the probability that exactly 10 have cable? what is the probability that at least 13 have cable? what is the probability that fewer than 13 have cable?

  5. Binomial Probability Distribution (take 2) Find table II in the back of your book. Find when n = 15 and p(x) = .70. Redo the 3 problems we just did by hand. WOW!!!

  6. Binomial Probability Distribution (take 3) On your graphing calculator, find the DISTR button. Under its menu, find binompdf( and binomcdf( If 20% of US women attended a musical in 2002, in a random sample of 15 women, 1. What is the probability that EXACTLY 5 attended a musical in 2002? 2. What is the probability that FEWER THAN 7 attended a musical in 2002?

  7. Practice According to American Airlines, its flight 215 from Orlando to Los Angeles in on time 90% of the time. Suppose 15 flights are randomly selected and the number of on time flights is recorded. • Is this a binomial experiment? • What is the probability that exactly 14 of the flights are on time? • What is the probability that fewer than 14 flights are on time? • What is the probability that between 12 and 14 flights, inclusive, are on time?

  8. Mean and Standard Deviation To find the mean of a binomial random variable To find the standard deviation of a binomial random variable

  9. Practice For that same flight from Orlando, compute the mean and standard deviation of on-time flights in 100 trials of the probability experiment.

  10. Compute these probabilities. n = 10, p = 0.4, x = 3 0.2150 n = 50, p = 0.02, x = 3 0.0607 n = 9, p = 0.2, x < 3 0.9144 n = 20, p = 0.7, x > 12 0.8867

  11. Compute the mean and standard deviation N = 6, p = 0.3 1.8; 1.1 N = 10, p =0.2 2, 1.3 Assignment: page 340 19, 25, 27, 30, 31, 36 – 42, 44 – 48

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