Question

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.

Answer 1

Answer:

Given,

To determine the probability that more than 80% of sampled inhabitants are animals

p = 70% = 0.70

n = 120

p^ = 80% = 0.80

P(p^ > 0.80) = ?

let us consider,

P(z > (p^-p)/sqrt(pq/n) )

substitute the given values

= P(z > (0.80 - 0.70)/sqrt(0.70(1-0.70)/120) )

= P(z > 0.10/0.041833)

= P(z > 2.3905)

= 0.0084127

= 0.0084

So the probability that more than 80% of the sampled inhabitants are animals is 0.0084 .