1 / 24

Binomial Distributions

Binomial Distributions. Characteristics and Examples. 3 Characteristics:. 1) An event is repeated several times. 3 Characteristics:. An event is repeated several times Each event has only two possible outcomes, success or failure. 3 Characteristics:. An event is repeated severa l times

weldon
Télécharger la présentation

Binomial Distributions

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. Binomial Distributions Characteristics and Examples

  2. 3 Characteristics: 1) An event is repeated several times

  3. 3 Characteristics: • An event is repeated several times • Each event has only two possible outcomes, success or failure

  4. 3 Characteristics: • An event is repeated several times • Each event has only two possible outcomes, success or failure • All events are independent of each other i.e. the chance of success and failure remains constant for each event.

  5. There is a 5% chance that any apple in a bin of apples will have a blemish. If a sample of 25 apples is taken, find the probability that exactly 3 of the apples have blemishes. Is this an example of Binomial Distribution?

  6. There is a 5% chance that any apple in a bin of apples will have a blemish. If a sample of 25 apples is taken, find the probability that exactly 3 of the apples have blemishes. • The event of checking for blemishes will be repeated 25 times.

  7. There is a 5% chance that any apple in a bin of apples will have a blemish. If a sample of 25 apples is taken, find the probability that exactly 3 of the apples have blemishes. • The event of checking for blemishes will be repeated 25 times. • We can label the apple being blemished as success. The only other outcome (not blemished) can be labelled failure.

  8. There is a 5% chance that any apple in a bin of apples will have a blemish. If a sample of 25 apples is taken, find the probability that exactly 3 of the apples have blemishes. • The event of checking for blemishes will be repeated 25 times. • We can label the apple being blemished as success. The only other outcome (not blemished) can be labelled failure. • The events are independent as the rate of success remains 0.05 throughout. Therefore, this is a Binomial Distribution!

  9. Binomial Distribution Notation & Formula X is binomially distributed Probability of success Number of Trials

  10. Binomial Distribution Notation & Formula Failure = q = 1 - p

  11. There is a 5% chance that any apple in a bin of apples will have a blemish. If a sample of 25 apples is taken, find the probability that exactly 3 of the apples have blemishes.

  12. There is a 5% chance that any apple in a bin of apples will have a blemish. If a sample of 25 apples is taken, find the probability that exactly 3 of the apples have blemishes.

  13. There is a 5% chance that any apple in a bin of apples will have a blemish. If a sample of 25 apples is taken, find the probability that exactly 3 of the apples have blemishes.

  14. There is a 5% chance that any apple in a bin of apples will have a blemish. If a sample of 25 apples is taken, find the probability that exactly 3 of the apples have blemishes.

  15. There is a 5% chance that any apple in a bin of apples will have a blemish. If a sample of 25 apples is taken, find the probability that less than 3 of the apples have blemishes.

  16. There is a 5% chance that any apple in a bin of apples will have a blemish. If a sample of 25 apples is taken, find the probability that less than 3 of the apples have blemishes. For this question we need to find the probability of there being 2 blemishes, 1 blemish and no blemishes and add them together!

  17. There is a 5% chance that any apple in a bin of apples will have a blemish. If a sample of 25 apples is taken, find the probability that less than 3 of the apples have blemishes.

  18. There is a 5% chance that any apple in a bin of apples will have a blemish. If a sample of 25 apples is taken, find the probability that less than 3 of the apples have blemishes.

  19. An alternative question…

  20. There is a 5% chance that any apple in a bin of apples will have a blemish. If a sample of 25 apples is taken, find the probability that 3 or more of the apples have blemishes. For this question we must find the probability that blemishes appear on 3, 4, 5, 6, 7, 8 ….., 25 of the apples and add this all together!

  21. There is a 5% chance that any apple in a bin of apples will have a blemish. If a sample of 25 apples is taken, find the probability that 3 or more of the apples have blemishes. For this question we must find the probability that blemishes appear on 3, 4, 5, 6, 7, 8 ….., 25 of the apples and add this all together! Alternatively, we could find the probability of 2, 1 or zero (less than 3) blemishes and deduct it from 1!

  22. There is a 5% chance that any apple in a bin of apples will have a blemish. If a sample of 25 apples is taken, find the probability that 3 or more of the apples have blemishes.

  23. There is a 5% chance that any apple in a bin of apples will have a blemish. If a sample of 25 apples is taken, find the probability that 3 or more of the apples have blemishes.

  24. Now try: Exercise 29E Odd number questions

More Related