Answer Happy

6. In a factory quality controls are made for each of the items on the production line. Four independent tests are applied during the quality control and the failure rates for those tests are 0.02, 0.03, 0.02 and 0.04, respectively. The items that are failing any of those tests will be rejected. (a) (2 points) For a randomly selected item what is the probability that it is rejected? O 0.11567552 O 0.20567552 ✓ 0.10567552 O 0.08567552 O 0.17567552 O 0.06567552 O 0.16567552 O 0.13567552 O 0.09567552 O 0.21567552 (b) (2 points) For a randomly selected item what is the probability that it fails test 2 or test 3? O 0.0486 0.0466 0.0468 O 0.0497 O 0.0474 0.0483 O 0.0490 O 0.0456 ✓ 0.0494 O 0.0498 (c) (2 points) Given that the item we selected is rejected what is the probability that it fails test 2 or test 3? 0.38746872 O 0.51746872 O 0.48746872 O 0.43746872 O 0.54746872 O 0.62746872 O 0.56746872 ✓ 0.46746872 O 0.33746872 O 0.49746872
8. (4 points) In a supermarket 21% of the customers buy cleaning equipment. At the su- permarket 25% of the time the cleaning equipment are on sale. Given that the cleaning equipment are on sale, 34% of the customers buy them. Given that a customer bought cleaning equipment, what is the probability that the cleaning equipment are on sale at the time? 0.5747619048 ✓0.4047619048 O 0.3947619048 O 0.3647619048 O 0.4347619048 O 0.4747619048 O 0.5447619048 O 0.2947619048 9. (4 points) Suppose X is a continuous random variable whose probability density func- tion is f(x) = kx¹/³; 0< X<8. What is the mean value µx? (Hint: First find the constant k.) O 16/9 O 32/932/7 O 16/5 O 24/5 O 40/3 O 36/7 O 24/7