Mathematics, 24.09.2020 16:01 glogaming16
Alice knows that 70% of the creatures in Wonderland are anthropomorphic animals. She randomly invites several of Wonderland’s inhabitants to a tea party. Depending on which inhabitants of Wonderland are chosen, the proportion of animals invited may vary. If Alice samples 120 inhabitants, what is the probability that more than 80% of the sampled inhabitants are animals? Give your answer to four decimal places.
Answers: 2
be the sample proportion of the creatures are anthropomorphic animals.![P(\hat{p}0.80)=P(\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\dfrac{0.80-0.70}{\sqrt{\dfrac{0.70\times (1-0.70)}{120}}})\\\\P(\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\dfrac{0.10}{\sqrt{\dfrac{0.70\times 30}{120}}})\\\\ =P(Z\dfrac{0.10}{\sqrt{0.00175}})\ \ \ \ \ [Z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}]\\\\ =P(Z\dfrac{0.10}{0.04183})\\\\\=P(Z2.39)\\\\=1-P(Z\leq2.39)\\\\=1- 0.9916= 0.0084](/tpl/images/0778/8885/c9d9c.png)
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Alice knows that 70% of the creatures in Wonderland are anthropomorphic animals. She randomly invite...
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