Pure Water Supplies water machines to offices.Part of routine maintenance, water samples from each of its machines are monthly tested for bacteria.If positive for bacteria, machine is taken to be cleaned.Test is accurate and identify bacteria.The test is costly.PW is thinking about using it.Client has a two story building w/ 8 machines and 4 on first level and 4 on second level.Any month there is a 5% chance that any machine in the building will have bacteria and the presence of bacteria in each dispensing machine are independent events.PW's practice to test each machine in the office, once a month.8 tests per month.Testing regime water sample from the machines on each floor would be combined into a pooled sample and the pooled sample for each floor therefore will be tested.Test reveals the presence of bacteria, all four machines contributing to that sample are then tested again.

If both pool samples test result in a negative test for bacteria, then all machines would be free of bacteria in two tests.If bacteria is detected, additional tests will be required:

1)Let N be a random variable, dnoting the number of tests that will be done under the testing scenario?Write out the probability table for N

2)The expected value of N?

3)Standard deviation of N?

4)If the client has 20 floors, with four dispensing machines on each floor?All other data is the same as above.What is the expected the number of tests needed if it uses the pooled testing strategy applied to 20 floors: Testing one pooled sample per floor, retesting machines contribute to a pool when that pooled test reveals the presence of bacteria