C. of the total It is known that, in a certain manufacturing process, 1% of the

Question

C. of the total

It is known that, in a certain manufacturing process, 1% of the products are defective. Wa 100 of these products selected at random: purchanes a. (0.S points) What is the probability of having at least one defective product in this b. (0.8 points) hat is the expected valu ints) What is the probability of having at least one defective product in this purchase 8 points) What is the expected value and standard deviation of the number of defects? 0.8 points) The col n pany has a policy of replacing, free-of-charge, all defective products th atar purchased. If each replacement costs the company $20, what is the expected value of the w c. replacement cost for these 100 products (Hint: E 20X)?)?

Explanation / Answer

This problem can be solved by using the binomial distribution where No. of products, n = 100, probability of defect, p = 0.01

Thus, q = 1 - p = 0.99

Let X denote the number of defective products.

(a) P(X>=1) = 1 - P(X=0) = 1 - (0.99)^100 = 0.634

(b) Expected value of the number of defects , E[X] = np = 100*0.01 = 1

Standard deviation of number of defects = ?(npq) = ?(100*0.01*0.99) = 0.995

(c) To find E(20X) = 20*E(X) = 20*1 = 20

Expected value of replacement costs for 100 products = $20

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