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Binomial Probability Distribution: Pick up a note sheet from the front

Binomial Probability Distribution: Pick up a note sheet from the front. In a binomial experiment,. There are TWO mutually exclusive outcomes, often referred to as “success” and “failure”. If the probability of success is p , the probability of failure is 1 – p .

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Binomial Probability Distribution: Pick up a note sheet from the front

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  1. Binomial Probability Distribution: Pick up a note sheet from the front

  2. In a binomial experiment, There are TWO mutually exclusive outcomes, often referred to as “success” and “failure”. If the probability of success is p, the probability of failure is 1 – p.

  3. In a binomial experiment, we can compute probabilities of certain outcomes. For a binomial experiment to occur, these four conditions must be met: • There are a fixed number of observations (n). • Each observation is independent. • Ex: In a situation where tossing a coin, the 5th toss is not dependent on any of the previous 4 tosses. They are independent! • Each observation falls into only TWO categories: success and failure. • Probability of success is labeled p • Probability of failure is labeled 1-p • The probability of success, p, is the same for each of the n observations.

  4. The probability of an event, p, occurring exactly r times: nCr C = combination (order does not matter) n = # of trials r = # of specific events you wish to obtain (may also be called x) p = probability of success q = probability of failure (1-p)

  5. #1Eight out of every 10 persons who contract a certain viral infection can recover. If a group of 9 people become infected, what is the probability that exactly 5 people will recover?

  6. For P(x = r), use binompdf(n,p,r) Note: r refers to some number of successes between 0 and n. 2ndVars: A:binompdf(n, p, r)

  7. #2In Lisa’s art class, 1 out of 5 paintings that she makes will be chosen for an art show. If she is preparing 9 paintings for the competition, what is the probability that exactly 2 of them will be chosen?

  8. #3Assume that 60% of marigold seeds that are sown directly in the ground produce plants. If Big Bird plants 10 seeds, what is the probability that • at least 7 plants will grow? • at most 2 plants will grow?

  9. In the calculator: For any situation other than P(x = r), use 2ndVars: B: binomcdf( • To find P(x ≤ r), use binomcdf(n, p, r) • To find P(x < r), use binomcdf(n, p, r – 1) • To find P(x > r), use 1-binomcdf(n, p, r) • To find P(x ≥ r), use 1-binomcdf(n, p, r – 1) • Note: r refers to some number of successes between 0 and n.

  10. Mean and Standard Deviation of a Binomial Distribution Formulas: Mean: Standard Deviation:

  11. A basketball player has a free throw percentage of 75%. In a single game, the player shoots 12 free throws. Find the mean and standard deviation for this player.

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