1. Warm Up
Industrial quality control programs often inspect a small sample of incoming parts. If any parts in the sample are found to be defective, the shipment is held for more detailed inspection; if all the parts sampled are good the shipment is released to production. Imagine a company samples 20 parts from a shipment of ) Assume we know 5% of the 1000 parts are actually defective. What is the probability at least 1 defective part will be found in the sample? 2) Assume we know 10% of the 1000 parts are actually defective. What is the probability at least 1 defective part will be found in the sample?

2. Example
Assume we know 75% of the cars at a smog inspection station pass the smog test. If we take repeated random samples of 50 cars and count the number of passing cars: 1) Can we approximate the distribution as normal? 2) Find the mean and standard deviation of the number of cars that pass inspection in a sample of size 50. 3) Using a normal approximation, what is the probability that at least 40 cars in the sample will pass the smog test?

3. Practice
Approximately 2% of births in the U.S. are considered premature (before 34 weeks). If we take repeated random samples of 1000 births and count the number of premature births: 1) Is this binomial distribution approximately normal? 2) What are the mean and standard deviation of the number of births that are premature in the sample of 1000 births? 3) What is the probability that at least 10 of the births in the sample are premature (use a normal approximation)?

4. Practice Continued
Approximately 2% of births in the U.S. are considered premature (before 34 weeks). If we take repeated random samples of 1000 births and count the number of premature births: 4) Calculate your answer to problem #3 by using a binomial distribution. How do the answers compare? Why are they different?

5. Practice
Zoe the dog is learning to catch a frisbee. Right now Zoe is not very good and only catches 15% of the throws. 1) What is the probability that it will take exactly 3 throws for Zoe to catch the frisbee? 2) What is the probability Zoe will not catch the frisbee in the first 5 throws? 3) In the long run, how many throws will you need to make before Zoe’s first catch?