AP Statistics Chapter 17
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)
Bernoulli trials must be independent.
It is only okay to proceed if the sample is smaller than 10% of the population.
- 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