A certain company produces vinyl for records in three grades (A, B, and C). Over time, grade A vinyl has a 3% defective rate, grade B vinyl has a 5% defective rate, and grade C vinyl has a 10% defective rate. Since grade A vinyl is less likely to be defective, the company can charge more money than it can charge for the other two grades. The company can also charge more money for grade B vinyl than grade C vinyl.
Recently, the company found a batch of unlabeled vinyl in a warehouse. They could determine the vinyl was from the same batch. The company randomly sampled 150 discs and found 8 defective discs.
(a) Construct and interpret a 90% confidence interval for the proportion of defective discs in the batch.
(b) Does the interval calculated in part (a) clearly allow the company to determine the grade of the vinyl?
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