Question: The Write Right Company manufactures ballpoint pens and has been experiencing a 5% rate of defective pens. Modifications are made to the manufacturing process in an attempt to improve quality, and the manager claims that the modified procedure is better, because a test of 50 pens shows that only one is defective.

a. Assuming that the 5% rate of defects has not changed, find the probability that among 50 pens, exactly one is defective.

b. Assuming that the 5% rate of defects has not changed, find the probability that among 50 pens, none are defective.

c. What probability value should be used for determining whether the modified process results in a defect rate is than 5%.

d. What do you conclude about the effectiveness of the modified production process?