Answer: 0.0084
Step-by-step explanation:
Let p be the population proportion of the creatures in Wonderland are anthropomorphic animals.
As per given, p = 0.70
Sample size : n=120
Let [tex]\hat{p}[/tex] be the sample proportion of the creatures are anthropomorphic animals.
Now, required probability :
[tex]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(Z>2.39)\\\\=1-P(Z\leq2.39)\\\\=1- 0.9916= 0.0084[/tex]
Hence, the probability that more than 80% of the sampled inhabitants are animals= 0.0084
