Items are examined sequentially at a manufacturing plant. The probability that an item is defective is 0.05. (a) What is the probability that the first 20 items examined are not defective? (b) What is the expected number of examined items until we get the fifth defective?
Items are examined sequentially at a manufacturing plant. The probability that an item is defective is...
Problem 2. The Hit-and-Miss Manufacturing Company produces items that have a probability p of being defective. These items are produced in lots of 150. Past experience indicates that p for an entire lot is either 0.05 or 0.25. Furthermore, in 90 percent of the lots produced, p equals 0.05 (so p equals 0.25 in 10 percent of the lots). These items are then used in an assembly and ultimately their quality is determined before the final assembly leaves the plant....
A machine is operating at rate of 10% defective items. If each item is inspected as it is produced, find the probability that the first defective item found is the fifth item inspected.
Suppose machine 1 produces items that are independently defective with probability 0.01, machine 2 produces items that are independently defective with probability 0.02, and machine 3 produces items that are independently defective with probability 0.04. Suppose we purchase a box with 100 items in it, all of which were produced by the same machine. The box was produced by machine 1 with probability 0.5, by machine 2 with probability 0.3, and by machine 3 with probability 0.2. (a) Find the...
20% of the items on a production line are defective. Randomly insptect items, and let X1 be the number of inspections till the first defective item is observed, and X5 be the number of inspections till the fifth defective item is observed. In both cases, X1 and X5 inlcude the defective item itself (e.g. if the items are {good, good, defective), X1 is 3). Calculate E (%). V (Xs)
When a particular machine is functioning properly, 80% of the items produced are non-defective. If 3 items are examined, what is the probability that one is defective?
Homework Assigment - Quality Control Problem: We know that the probability of an item being defective, p, can only be .05,.1 or .2. However, we have no additional information on which on if these three is more likely If we test items until a defective item has been found, what is the probability that p is .05, .1 or .2 given you had to test 1, 2, 3, 4 or 5 items (I am asking for 135 posterior probabilities)? Setup...
A manufacturing process produces 5.5% defective items. What is the probability that in a sample of 51 items: a. 11% or more will be defective? (Round the z-value to 2 decimal places and the final answer to 4 decimal places.) Probability b. less than 1% will be defective? (Round the z-value to 2 decimal places and the final answer to 4 decimal places.) Probability c. more than 11% or less than 1% will be defective? (Round...
A manufacturing process produces 6.4% defective items. What is the probability that in a sample of 49 items: a. 10% or more will be defective? (Round the z-value to 2 decimal places and the final answer to 4 decimal places.) Probability b. less than 2% will be defective? (Round the z-value to 2 decimal places and the final answer to 4 decimal places.) Probability c. more than 10% or less than 2% will be defective? (Round...
A manufacturing process produces 5.8% defective items. What is the probability that in a sample of 52 items: a. 9% or more will be defective? (Round the z-value to 2 decimal places and the final answer to 4 decimal places.) Probability b. less than 2% will be defective? (Round the z-value to 2 decimal places and the final answer to 4 decimal places.) Probability c. more than 9% or less than 2% will be defective? (Round the z-value to 2...
6. Suppose that the proportion 0 of defective items in large shipment is unknown and that the prior distribution of 0 is the beta distribution with parameters 1 and 10. Assume in a random sample of 20 items that 1 item is found to be defective. (a) What is the expected value and variance of the prior distribution? (b) What is the posterior distribution? (c) What is the Bayes estimator for 0 if one uses the quadratic loss function? (d)...