7. You've just been hired on at the newly opening cookie factory in Springfield as a quality control specialist. The factory
is installing equipment that is known to produce cookies with a 4.5% defect rate. As a quality control specialist, it is your
job to determine when maintenance must be completed on the machinery. If a sample of 175 cookies has more than 15
defective cookies, then the machinery needs to be calibrated.
a. How many cookies should you expect to be defective in a sample of 175? (2 points)
b. What is the probability that more than 15 cookies are defective if the machinery is working properly? (2 points)
c. What is the probability that a sample has exactly 6 defective cookies when the machinery is working properly?
(2 points)
d. The next day after calibrating the machinery, you take a sample and find that 18 of 175 cookies are defective.
What conclusion can you draw from this result? Support your answer with a probability value. (4 points)