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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

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Binomial Distributions

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  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

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