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# AP Statistics Chapter 17

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Conditions for Bernoulli Trials
1. There are two possible outcomes (success and failure).
2. the probability of success, p, is constant.
3. the trails are independent.

Ex. Flipping a coin; rolling a die and noting whether or not it came up as a six.
Geometric probability model
- Tells us the probability for a random variable that counts the number of Bernoulli trials UNTIL THE FIRST SUCCESS
- Denoted by: Geom(p)
Mean & Standard Deviation of Geometic model
Mean = 1/p
SD = sqrt(q)/p
Binomial probability model
- Tells us the probabilty for a random variable that counts the NUMBER OF SUCCESSES in a fixed number of Bernoulli trials.
- Denoted by: Binom(n,p)
Mean & Standard Deviation of Binomal model
Mean = np
SD = sqrt(npq)
10% Condition
Bernoulli trials must be independent.
It is only okay to proceed if the sample is smaller than 10% of the population.
Success/Failure condition
- A binomal model is approximately Normal if we expect at least 10 successes and 10 failures:
np > or equal to 10 and nq > or equal to 10
Difference between Geometric and Binomial models
- Both involve Bernoulli trials, but the issues are different.
- Geometric probability = trials until first success
- Binomial probability = number of successes in a specified number of trials
Difference between Normal and Binomial models
- Binomial gives probabilities for a specific count
- Normal gives continous random variable that can take place on any value