In: Statistics and Probability
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 8% 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 10%. [You may find it useful to reference the z table.]
a. What is the probability that the production machines will be adjusted if the batch consists of 65 items? (Round “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 77 items? (Round “z” value to 2 decimal places, and final answer to 4 decimal places.)