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Chapter 17 and 18 outline Chapter 17: Bernoulli Trialsa. there are two possible outcomes b. the probability of success is constant c. the trials are independent Geometric Setting: Geometric probability model – geometpdf vs geometcdf p= success and q= failure X= the number of trials until the first success occurs 𝑃(𝑋 = 𝑥) = 𝑞 𝑥−1 𝑝 1 mean= 𝜇 = 𝑝 𝑞 Standard deviation: 𝜎 = √𝑝2 Binomial Probability model- binomcdf vs binompdf Binomial setting: n=number of trials p=success and q=failure X=the number of successes in n trials 𝑛 𝑃(𝑋 = 𝑥) = ( ) 𝑝𝑘 𝑞𝑛−𝑘 𝑘 Mean: 𝜇 = 𝑛𝑝 Standard deviation: 𝜎 = √𝑛𝑝𝑞 Success/Failure condition: For a Normal model to be a good approximation of a Binomial model, we must expect at least 10 success and 10 failures. That is 𝑛𝑝 ≥ 10 𝑎𝑛𝑑 𝑛𝑞 ≥ 10 Chapter 18: Sampling distribution model Sampling distribution model for a proportion: As long as the conditions/assumptions are met: 1. Randomization 2. Independence (10% condition) 3. Success/Failure Use a sampling distribution model for a proportion with 𝜇𝑝̂ =p and 𝜎𝑥 = √ 𝑝𝑞 𝑛 Central Limit Theorem Sampling distribution model for a mean: As long as the conditions/assumptions are met: 1. Randomization 2. Independence (10% condition) 3. Large enough Use a sampling distribution model for a mean with 𝜇𝑦̅ = 𝜇 and 𝜎𝑦̅ = 𝜎 √𝑛 Standard error The 5 steps with each problem: 1. Conditions/Assumptions 2. State which model you will be using to model the situation 3. Draw out a Normal model with the appropriate mean, standard deviation, and area that you need to find. 4. State what you need to find in probability notation (eg: 𝑃(𝑋 < 2.4) 5. Conclusion in context