1 / 20

11A The Binomial Distribution

11A The Binomial Distribution. Are these Bernoulli sequences? Rolling an 8-sided die, numbered 1 to 8, 40 times and recording the number of 6s. Drawing a card from a fair deck, with replacement, and recording the number of aces. Rolling a die 60 times and recording the number obtained.

deepak
Download Presentation

11A The Binomial Distribution

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 11A The Binomial Distribution Are these Bernoulli sequences? Rolling an 8-sided die, numbered 1 to 8, 40 times and recording the number of 6s. Drawing a card from a fair deck, with replacement, and recording the number of aces. Rolling a die 60 times and recording the number obtained.

  2. 11A The Binomial Distribution OR

  3. 11A The Binomial Distribution A fair die is rolled 4 times and X is the event of rolling a 3.

  4. 11A The Binomial Distribution Pr (X = x) = nCxpxqn-x, where x = 0,1,2,…,n where x is the occurrence of the successful outcome

  5. 11A The Binomial Distribution A binomial variable, X, has the probability function Pr (X = x) = 6Cx(0.4)x (0.6)n-x, where x = 0,1,2,3,4,5,6. Find: n, the number of trials p, the probability of success, the probability distribution for x as a table. Pr (X = x) = nCxpxqn-x Pr(X = 0) = 6C0 (0.4)0 (0.6)6 Pr(X = 0) 0.046656 Pr(X = 1) = 6C1 (0.4)1 (0.6)5 Pr(X = 1) 0.186624 Pr(X = 2) 0.31104 Pr(X = 2) = 6C2 (0.4)2 (0.6)4 Pr(X = 3) = 6C3 (0.4)3 (0.6)3 Pr(X = 3) 0.27648 Pr(X = 4) = 6C4 (0.4)4 (0.6)2 Pr(X = 4) 0.13824 Pr(X = 5) = 6C5 (0.4)5 (0.6)1 Pr(X = 5) 0.036864 Pr(X = 6) 0.004096 Pr(X = 6) = 6C6 (0.4)6 (0.6)0

  6. 11A The Binomial Distribution A binomial variable, X, has the probability function Pr (X = x) = 6Cx(0.4)x (0.6)n-x, where x = 0,1,2,3,4,5,6. Find: n, the number of trials p, the probability of success, the probability distribution for x as a table. and so on and so on and … … …

  7. 11A The Binomial Distribution A fair die is rolled five times. Find the probability of obtaining: a. exactly four 5s, Pr (X = x) = nCxpxqn-x 5C4

  8. 11A The Binomial Distribution A fair die is rolled five times. Find the probability of obtaining: b. exactly 2 even numbers, 5C2

  9. 11A The Binomial Distribution A fair die is rolled five times. Find the probability of obtaining: c. all results greater than 3, 5C5 1

  10. 11A The Binomial Distribution A fair die is rolled five times. Find the probability of obtaining: d. a 5 on the first roll only,

  11. 11A The Binomial Distribution A new drug for hay fever is known to be successful in 40% of cases. Ten hay fever sufferers take part in the testing of the drug. Find the probability, to 4 decimal places, that; 4 are cured, nobody is cured, all 10 are cured. 10C4

  12. 11A The Binomial Distribution A new drug for hay fever is known to be successful in 40% of cases. Ten hay fever sufferers take part in the testing of the drug. Find the probability, to 4 decimal places, that; 4 are cured, nobody is cured, all 10 are cured. 10C0

  13. 11A The Binomial Distribution A new drug for hay fever is known to be successful in 40% of cases. Ten hay fever sufferers take part in the testing of the drug. Find the probability, to 4 decimal places, that; 4 are cured, nobody is cured, all 10 are cured. 10C10

  14. 11A The Binomial Distribution • The probability of scoring a bullseye on any one throw is 0.3. • if 6 shots are taken, find the probability, to 4 decimal places, that: • the bullseye is not hit on any shot, • the bullseye is hit at least once. • Find the number of throws to ensure a probability of more than 0.8 of hitting at least one bullseye. 6C0

  15. 11A The Binomial Distribution • The probability of scoring a bullseye on any one throw is 0.3. • if 6 shots are taken, find the probability, to 4 decimal places, that: • the bullseye is not hit on any shot, • the bullseye is hit at least once. • Find the number of throws to ensure a probability of more than 0.8 of hitting at least one bullseye.

  16. 11A The Binomial Distribution • The probability of scoring a bullseye on any one throw is 0.3. • if 6 shots are taken, find the probability, to 4 decimal places, that: • the bullseye is not hit on any shot, • the bullseye is hit at least once. • Find the number of throws to ensure a probability of more than 0.8 of hitting at least one bullseye.

  17. 11A The Binomial Distribution - graphs A fair die is rolled 4 times and X is the event of rolling a 3, .

  18. 11A The Binomial Distribution – graphs, changing p

  19. 11A The Binomial Distribution – graphs, changing n

  20. 11A The Binomial Distribution

More Related