In a process that manufactures bearings, 90% of the bearings meet a thickness specification. A shipment contains 500 bearings. A shipment is acceptable if at least 440 of the 500 bearings meet the specification. Assume that each shipment contains a random sample of bearings.
a. What is the probability that a given shipment is acceptable?
b. What is the probability that more than 285 out of 300 shipments are acceptable?