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