In: Math
a. Suppose that 5 % of the items produced by a factory are defective. If 5 items are chosen at random, what is the probability that none of the items are defective? Write your answer as a decimal accurate to three decimal places.
b. Suppose that 7.9 % of the items produced by a second factory are defective. If 5 items are chosen at random from the second factory, what is the probability that exactly one of the items is defective? Write your answer as a decimal accurate to three decimal place
c. Suppose that 10.8 % of the items produced by a third factory are defective. If 5 items are chosen at random from the third factory, what is the probability that exactly two of the items are defective? Write your answer as a decimal accurate to three decimal places.
d. Suppose that 7.3 % of the items produced by a fourth factory are defective. If 5 items are chosen at random from the fourth factory, what is the probability that at least two of the items are defective? Write your answer as a decimal accurate to three decimal places.
e. Suppose that 14.2 % of the items produced by a fifth factory are defective. If 4 items are chosen at random from the fifth factory, what is the expected value (or mean value) for the number of defective items? Write your answer as a decimal accurate to three decimal places.