When a company's production process malfunctions, it needs to make either a minor adjustment or a major adjustment. If the defective rate is 10%, then it needs to make a minor adjustment. If the defective rate is 25%, then it needs to make a major adjustment. For a sample of 20 units, the company observes the number of defects. It does not know what type of adjustment is needed.
a) What is the probability of observing 3 or fewer defects if a major adjustment is needed?
b) What is the probability of observing 4 or more defects if a minor adjustment is needed?