XYZ Inc. manufactures a unique fuel injection system that yields dramatic cost savings through improved fuel efficiency. The effectiveness of the system is dependent upon the quality of a specialized sensor. These sensors are purchased from an external supplier for $21 each. For the past few years, an average of 10% of the sensors purchased from the supplier have not met XYZ's quality requirements. The number of unusable sensors has ranged from 5% to 25% of the total number purchased and has resulted in failures in meeting production schedules. In addition, XYZ has incurred additional costs to replace the defective units because the rejection rate of the units is within the range agreed upon in the contract. XYZ is considering a proposal from its engineering department to manufacture the sensors internally. XYZ has the facilities and equipment to produce the components. The engineering department has designed a manufacturing system that will produce the sensors with a defect rate of 5% of the number of units produced. The following schedule presents the engineers' estimates of the probabilities that different levels of variable manufacturing cost per sensor will be incurred under this system. Additional annual fixed costs incurred by XYZ, if it manufactures the sensor, will amount to $42,500. Estimated variable manufacturing cost per sensor Probability of occurrence $12 10% $15 30% $18 40% $21 20% XYZ will need 18,000 sensors to meet its annual demand requirements. Formulate an expected-value analysis to determine whether XYZ should manufacture the sensors.