A certain company makes three grades (A, B,C) of a particular electrical component. Historically, grade A components have a 2% defective rate, grade B components have a 5% defective rate, and grade C components have a 10% defective rate. Since grade A components are less likely to be defective, the company can charge more money for those components than it can charge for the grade B or C components. Similarly, the company can charge more money for grade B components than it can charge for grade C components. Recently, the company found a batch of components in a warehouse that were known to be of the same grade, but the grade was not labeled on the components. To determine the grade (A, B,C) the company selected from that batch a random sample of 200 components, which contained 16 defective components.

a) Construct and interpret a 95% confidence interval for the proportion of defective components in the batch.

b) Does the interval calculated in part a allow the company to clearly determine the grade of component that was produced in the batch? Explain.