Question

A manufacturing firm produces a product that has a ceramic coating. The coating is baked on to the product, and the baking process is known to produce 5% defective items. Every hour, 20 products from the thousands that are baked hourly are sampled from the ceramic-coating process and inspected. Complete parts a through c. a. What is the probability that 5 defective items will be found in the next sample of 20? The probability is that 5 defective items will be found in the next sample of 20. (Round to four decimal places as needed.) b. On average, how many defective items would be expected to occur in each sample of 20? Each sample of 20 would be expected to have defective item(s). (Type an integer or a decimal.) c. How likely is it that 15 or more nondefective (good) items would occur in a sample due to chance alone? The probability that 15 or more nondefective (good) items would occur in a sample due to chance alone is approximately (Round to four decimal places as needed.)

Answer 1

Sal. I af defective items = 5% Now a sample of 20 items is selected sandomly Let'x' be a handom vanliable for the no.. og items that are defective 'x'follows binomial distribution with n = 20 3p = 0.05 X~Bin (20,0.05) (1) P ( x= 5) = 20 65 10.058(1-0.05) 20-5 z0.0022 my (b) E(X) = nap = 20 X 0.65 . I hy (C) P(1504 more non-defective goods) = P(x5) = 20cy (0-05)' (1-0.05) 5 20- X=0 = 0.9997 thy