Suppose that a concrete manufacturer has made 200 concrete cylinders that are supposed to withstand 4000 pounds per square inch of pressure. As the quality-control manager, you decide to randomly test four of the cylinders to be sure they are manufactured to specification. You will only accept the shipment if all four cylinders pass the inspection. What is the probability that the shipment is accepted:

(a) If 10% of the 200 cylinders are defective?

(b) If 20% of the 200 cylinders are defective?

(c) If 40% of the 200 cylinders are defective?

(d) If 60% of the 200 cylinders are defective?

(e) If 80% of the 200 cylinders are defective?

(f) Draw a horizontal axis and label it Percent Defective. Draw a vertical axis and label it Probability Accept Shipment. Plot probability accept shipment against the percent defective and connect the points in a smooth curve. This curve is referred to as an operating characteristic curve.