230 CHAPTER 5 Discrete Probability Distributions b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high. c. Is the result of 9 peas with green pods a result that is significantly high? Why or why not? 32. Hybrids Assume that offspring peas are randomly selected in groups of 16. a. Find the mean and standard deviation for the numbers of peas with green pods in the groups of 16. b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high. c. Is a result of 7 peas with green pods a result that is significantly low? Why or why not? Composite Sampling. Exercises 33 and 34 involve the method of composite sampling, whereby a medical testing laboratory saves time and money by combining blood samples for tests so that only one test is conducted for several people. A combined sample tests positive 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 in the United States, the proportion of people infected with the human immunodeficiency virus (HIV) is 0.00343. In tests for HIV, blood samples from 50 different people are combined. What is the probability that the combined sample tests positive for HIV? Is it unlikely for such a combined sample to test positive? 34. Workplace Drug Testing Workplace drug tests have an annual positive rate of 4.2% (based on data from Quest Diagnostics). Given that the rate is quite low, samples can be combined into groups of 100 and tested together. If the group fails, the individual samples can be retested to identify the particular workers who have positive test results. What is the probability that a combination of 100 samples yields a positive result? Based on the resulting probability, does it seem wise to combine 100 samples into one sample? Acceptance Sampling. Exercises 35 and 36 involve the method of acceptance sampling. With acceptance sampling, a large shipment of items is accepted or rejected based on test results from a sample drawn from the shipment. 35. Historical Use of Acceptance Sampling Methods of acceptance sampling were first used by the U.S. Army in World War II when batches of ammunition were accepted or rejected based on results from samples. A common World War II rifle was the M1, and it used 30 caliber ammunition, and an ammo can contains 500 rounds. Use this sampling plan: Randomly select and test 5 rounds from an ammo can, then accept the whole can if the number of defects is 0 or 1. If the true defect rate is 4%, what is the probability that an ammo can will be accepted? Based on the result, does it appear that there is a production problem with the ammo? 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 specifications. What is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected? Ultimate Binomial Exercises! Exercises 37–40 involve finding binomial probabilities, finding parameters, and determining whether values are significantly high or low by using the range rule of thumb and probabilities. 37. M&Ms Data Set 38 “Candies” in Appendix B includes data from 345 M&M candies, and 36 of them are brown. Mars, Inc. claims that 13% of its plain M&M candies are brown. For the following, assume that the claim of 13% is true, and assume that a sample consists of 345 M&Ms. a. For the 345 M&Ms, use the range rule of thumb to identify the limits separating numbers of brown M&Ms that are significantly low and those that are significantly high. Based on the results, is the result of 36 brown M&Ms significantly low?
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