(Solved): Acceptance sampling is an important quality control technique, where a batch of data is tested to d ...

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 $17\%$ 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 $21\%$. [You may find it useful to reference the $\underline{z}$ table. $]$ a. What is the probability that the production machines will be adjusted if the batch consists of 76 items? (Round final answer to 4 decimal places.) b. What is the probability that the production machines will be adjusted if the batch consists of 152 items? (Round final answer to 4 decimal places.)