Learning Outcomes: (a) Identify the binomial distribution *Highlight on binomial experiment (b) Find the mean and variance of binomial distribution (c) Find the probability by using binomial distribution At the end of the lesson, students should be able to Binomial Experiment (I) The experiment consists of n repeated trials. (II) Each trial has only two possible outcomes ["success" & "failure"] (III) The probability of "success", denoted p, is consistent for each trial. (IV) Each trial is independent. A binomial experiment is an experiment that has the following four properties: Binomial Distribution, The Binomial Distribution, is a discrete probability distribution of obtained from a binomial experiment with its function given by : • • • • • where • where • “Success” able to achieve the event stated in X Remarks: 9.1 Binomial Distribution C09 -SM025 Page 1
A fair coin is tossed three times. Find the probability of getting (a) no head, (b) exactly two heads, Solutions: Let (a) (b) Example 1 C09 -SM025 Page 2
(a) exactly 3 bulbs are damaged. (b) all bulbs are good. (c) not more than two bulbs are damaged. ** (d) at least one bulbs are damaged . In a box, 20% of bulbs are damaged. If a random sample of 10 bulbs is taken, find the probability that Solutions: Let (a) c u s e e (b) u s e u s e e (c) e u s e e (d) e s u s e Example 2 C09 -SM025 Page 3
Mean of Variance of • Standard deviation of • For , Example 3 A fair die is rolled 300 times. Let represents the number of times e u e ‘6’ s se ve . F e e s ev . Solution: Mean & Variance of Binomial Distribution C09 -SM025 Page 4
The table of Binomial Distribution is constructed based on the cumulative function given by the formula: for Interpretation from the Statistical table Based on the table above, for . Verification by calculation using formula: Table of Binomial Distribution C09 -SM025 Page 5
Let be a random such that . By using the binomial table, find Solution: Solution: Solution: Solution: Solution: Example 4 C09 -SM025 Page 6
To use Binomial Table for with convert into where . Example 5 Let X be a random variable such that . By using the binomial table, find Solutions: (a) (b) (c) Binomial Distribution with C09 -SM025 Page 7
Example 6 For a random variable X with a binomial distribution B(10, 0.45), find a when Solution: From table, Solution: From table, Others Binomial Distribution Problems C09 -SM025 Page 8