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%. Use Table 1.
a. What is the probability that the production machines will be adjusted if the batch consists of 50 items? (Round intermediate calculations to 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.)
b. What is the probability that the production machines will be adjusted if the batch consists of 100 items?