# While working in quality control, your job is to make sure that 95% of the 500 products which leave the factory each day are up to specifications. To test this, each day you select 25 products at rand

While working in quality control, your job is to make sure that 95% of the 500 products which leave the factory each day are up to specifications. To test this, each day you select 25 products at random and check their quality. If no more than one product is poor quality, it is considered acceptable. If two or more products are poor quality, you must test all 500 of the products manufactured that day, a costly and time-consuming process.

·         How can we write a binomial distribution which describes the process of selecting 25 products at random to test their quality, on a day which has 90% of the products up to specifications? Tell me about your process.

o    Why are the numbers 25 and 500 important, for assuming we can use a binomial distribution here?

o    What is the probability that your process will result in you incorrectly passing the products through quality control, mistakenly assuming the quality is at or above 95%? Tell me about your process.

·         What if we wanted to write a binomial distribution which describes the process of selecting 25 products at random to test their quality, on a day which has the required 95% of the products up to specifications? Tell me how this would change the distribution.

o    What is the probability that your process will result in you incorrectly assuming the quality is below 95%, and inspecting the entire day’s products unnecessarily? Tell me about your process.