A panel of people is assembled to test the ability to correctly distinguish an “improved” product from an older product. The panelists are chosen from a population consisting of 20% rural and 80% urban people. Two-thirds of the population are younger than 30 years of age, while one-third are older. The probability that the urban panelists under 30 years of age will correctly identify the improved product is 12%, while for older urban panelists, the probability increases to 45%. Regardless of age, rural panelists are twice as likely as urban panelists to correctly identify the improved product. a) What is the probability that any one panelist chosen at random from this population will correctly identify the improved product? b) For a panel of 10 persons, what is the expected number of panelists who will correctly identify the improved product? c) If a panelist has correctly identified the improved product, what is the probability that the panelist is under 30 years of age? d) If a panelist is under 30 years of age, what is the probability that the panelist will correctly identify the improved product?
A panel of people is assembled to test the ability to correctly distinguish an “improved” product from an older product. The panelists are chosen from a population consisting of 20% rural and 80% urban people. Two-thirds of the population are younger than 30 years of age, while one-third are older. The
a) What is the probability that any one panelist chosen at random from this population will correctly identify the improved product?
b) For a panel of 10 persons, what is the expected number of panelists who will correctly identify the improved product?
c) If a panelist has correctly identified the improved product, what is the probability that the panelist is under 30 years of age?
d) If a panelist is under 30 years of age, what is the probability that the panelist will correctly identify the improved product?
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