34 and 36

ete Probability Distributions if at least one person has the disease. If a combined sample tests positive, then individual blood tests are used to identify the individual with the disease or disorder. 33. HIV It is estimated that worldwide, 1% of those aged 15-49 are infected with the human immunodeficiency virus (HIV) (based on data from the National Institutes of Health). In tests for HIV, blood samples from 36 people are combined. What is the probability that the com- bined sample tests positive for HIV? Is it unlikely for such a combined sample to test positive? 34. Anemia Based on data from Bloodjournal.org, 10% of women 65 years of age and older have anemia, which is a deficiency of red blood cells. In tests for anemia, blood samples from 8 women 65 and older are combined. What is the probability that the combined sample tests positive for anemia? Is it likely for such a combined sample to test positive? Acceptance Sampling. Exercises 35 and 36 involve the method of acceptance sampling, whereby a shipment of a large number of items is accepted based on test results from a sample of the items. 35. Aspirin The MedAssist Pharmaceutical Company receives large shipments of aspirin tab- lets and uses this acceptance sampling plan: Randomly select and test 40 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If one shipment of 5000 aspirin tablets actually has a 3% rate of defects, what is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected? 36. AAA Batteries AAA batteries are made by companies including Duracell, Energizer, Eveready, and Panasonic. When purchasing bulk orders of AAA batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select 50 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 2 batteries do not meet specifications. A shipment contains 2000 AAA batteries, and 2% of them do not meet specific cations. What is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected