Question: A retail lumberyard routinely inspects incoming shipments of lumber from suppliers. For select grade 8-foot 2-by-4 pine shipments, the lumberyard supervisor chooses one gross (144 boards) randomly from a shipment of several tens of thousands of boards. In the sample, 18 boards are not salable as select grade.

(a) Calculate a 95% confidence interval for the proportion of boards in the entire shipment that is not salable as select grade.

(b) If 20% or more of the shipment is not salable as select grade, the shipment is not profitable. Just from looking at the interval values in part a) explain why the shipment is or is not profitable.