# Get out Homework from yesterday and have questions ready! BINOMIAL PROBABILITY DISTRIBUTION PICK UP A NOTES SHEET FROM THE FRONT TABLE! 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.

In a binomial experiment, we can compute probabilities of certain outcomes. For a binomial experiment to occur, these four conditions must be met: 1. There are a fixed number of observations (n). 2. Each observation is independent.

- 3. Each observation falls into only TWO categories: success and failure. -

4. Ex: In a situation where tossing a coin, the 5th toss is not dependent on any of the previous 4 tosses. They are independent! 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. The probability of an event, p, occurring exactly r times: In the calculator: binompdf(n,p,r) Note: r refers to some number of successes between 0 and n. 2nd Vars: A:binompdf(n, p, r)

n = # of trials p = probability of success r = # of specific events you wish to obtain (may also be called x) #1 Eight 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? #2 In Lisas 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?

Math III Warm Up 4/30/14 1. If Jim Bob makes a 35 on his Spanish test with a mean of 30

and a standard deviation of 2, did he do better that Dixie who made a 76 on her English exam with a mean of 74 and a standard deviation of 3? 2. 2 out of fifteen students fail a class their freshman year. What is the probability that out of a group of 10, exactly 3 freshmen will fail a class?

#3 Assume 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 a) at least 7 plants will grow? b) at most 2 plants will grow?

In the calculator: For any situation other than P(x = r), use 2nd Vars: 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. Mean and Standard Deviation of a Binomial Distribution Formulas: Mean:

Standard Deviation: 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.