Acceptance sampling is an important quality control technique, where a batch of data is tested to determine if the proportion of units having a particular attribute exceeds a given percentage. Suppose that 10% of produced items are known to be nonconforming. Every week a batch of items is evaluated and the production machines are adjusted if the proportion of nonconforming items exceeds 15%.
a. What is the probability that the production machines will be adjusted if the batch consists of 50 items?
b. What is the probability that the production machines will be adjusted if the batch consists of 100 items?