A manufacturer of pencils has 60 dozen pencils randomly chosen from each day's production and checked for defects. A defect rate of 10% is considered acceptable.

a)Assuming that 10% of all the manufacturer's pencils are actually defective, what is the probability of finding 80 or more defective pencils in this sample?

b)If 110 pencils are found to be defective in today's sample, is it likely that the manufacturing process needs improvement? Explain your conclusion.