1. 4.2 Binomial Distributions I.Binomial Experiments A binomial experiment is a probability experiment that satifies the following conditions: 1. Fixed number of independent trials 2. Only 2 possible outcomes: success/failure 3. P(s) is the same for each trial 4. The random variable x counts the number of successful trials

2. Notation nthe # of times a trial is repeated p = P(s)the probability of success in a single trial q = P(f)q = 1 – p ; probability of failure xthe number of successes in n trials

3. II. Binomial Probability Formula In a binomial experiment, the probability of exactly x successes in n trials is: P(x) = n C x ∙ p x ∙ q n-x Now read example 2 (p186) and complete TIY#2

4. HW: p194-195 #6, 8, 14a, 20a, 22a

5. Binomial Probability Distribution: the list of all possible values of x with the corresponding probability of each Read example 3 (p187) and complete TIY#3.

6. III. Finding Binomial Probabilities There is a way to do this on your TI-83+ calculator! –Press 2 nd VARS to get to your distribution menu; scroll down to 0:binompdf( –Then you enter n, p, x) P188 Do example 4 & TIY#4

7. Now how is example 5 different? At least or less than problems use a different command in the calculator. In the DIST menu select A:binomcdf(n, p, x) This will add up all probabilities starting with 0 and ending at x. Do example 5 and TIY#5

8. There is a table….will you use it??? IV.Graphing Binomial Probabilities I.Same process as a discrete probability distribution Example 7 p191 Now do TIY#7 on a piece of graph paper and submit.

9. Graphing binomial distributions continues…. Skewed left: p> 0.5 Skewed right: p< 0.5 Symmetric: p = 0.5 HW: p193-195 #2, 4, 14b&c, 20b&c, 22b&c

10. V.Mean, Variance, and Standard Deviation The formulas are much simpler for a binomial distribution Mean: μ = np Variance: σ 2 = npq Standard deviation: σ = √ npq P192 Example 8 & TIY#8

11. HW: p194-195 #10, 12, 16, 18, 20d,e,f, 22d,e,f