Country A and its neighboring Country B are very competitive, both claiming that a higher percentage "smart" people. So an experiment is conducted. A "smart" test is given to random samples in each country. Here are the results... Total Tested Number who were "smart" Country A 100 80 Country B 100 85 Based on these samples, Country B claims superiority. A social media frenzy ensues! For the purposes of this problem, assume that Country A and Country B actually have the same percentage of smart people, and that the results above -- seeming to favor Country B -- were just a result of random differences in sampling. Under that assumption, if the experiment were conducted again (100 new randomly selected people from each country), find the probability that Country B would once again "win" by 5% or more. Round to three decimal places, for example 0.286
Country A and its neighboring Country B are very competitive, both claiming that a higher percentage "smart" people. So an experiment is conducted. A "smart" test is given to random samples in each country. Here are the results...
| Total Tested | Number who were "smart" | |
| Country A | 100 | 80 |
| Country B | 100 | 85 |
Based on these samples, Country B claims superiority. A social media frenzy ensues!
For the purposes of this problem, assume that Country A and Country B actually have the same percentage of smart people, and that the results above -- seeming to favor Country B -- were just a result of random differences in sampling.
Under that assumption, if the experiment were conducted again (100 new randomly selected people from each country), find the probability that Country B would once again "win" by 5% or more.
Round to three decimal places, for example 0.286
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