A furniture manufacturer performs final inspections on furniture pieces produced. The pieces are classified as follows with associated probabilities: flawless (0.90 probability), with cosmetic flaws

(0.08 probability), and flawed requiring rework (0.02 probability). Assume that the pieces are independent,

(a) What is the probability of producing 20 flawless pieces out of 20 produced in a day?

(b) What is the probability of producing at least one piece with cosmetic flaws out of 20 produced in a day?

(c) What is the probability of producing at least one piece with flaws out of 20 produced in a day?

(d) What are the mean and standard deviation of the number of flawless pieces produced in a day?