3. [-/5 Points] DETAILS DEVORESTAT9 5.E.008. ASK YOUR TEACHER PRACTICE ANOTHER A stockroom currently has 30 components of a certain type, of which 12 were provided by supplier 1, 8 by supplier 2, and 10 by supplier 3. Six of these are to be randomly selected for a particular assembly. Let X = the number of supplier 1's components selected, Y = the number of supplier 2's components selected, and p(x, y) denote the joint pmf of X and Y. (a) What is p(1, 3)? [Hint: Each sample of size 6 is equally likely to be selected. Therefore, p(1, 3) = (number of outcomes with X = 1 and Y = 3)/(total number of outcomes). Now use the product rule for counting to obtain the numerator and denominator.] (Round your answer to five decimal places.) p(1, 3) = (b) Using the logic of part (a), obtain p(x, y). (This can be thought of as a multivariate hypergeometric distribution-sampling without replacement from a finite population consisting of more than two categories. Round your answers to five decimal places.) X P ( x , y ) 3 5 6 0 N Y A 6 Need Help? Read It Talk to a Tutor Viewing Saved Work Revert to Last Responselargest 10% 42.112 mm You may need to use the appropriate table in the Appendix of Tables to answer this question. Need Help? Read It Talk to a Tutor [0/4 Points] DETAILS PREVIOUS ANSWERS DEVORESTAT9 4.E.054. ASK YOUR TEACHER PRACTICE ANOTHER Suppose that 14% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped). Consider a random sample of 200 shafts, and let X denote the number among these that are nonconforming and can be reworked. (Round your answers to four decimal places.) (a) What is the (approximate) probability that X is at most 30? 0.6582 X (b) What is the (approximate) probability that X is less than 30? 0.6582 X (c) What is the (approximate) probability that X is between 15 and 25 (inclusive)? 0.2637 X You may need to use the appropriate table in the Appendix of Tables to answer this question. Need Help? Read It Talk to a Tutor