3- In a certain population of mussels (mytillus edulis) 80% of the individuals a

Question

3- In a certain population of mussels (mytillus edulis) 80% of the individuals are infected with an intestinal parasite. A marine biologist plans to examine 100 randomly chosen mussels from the population.
A) Find the probability that 85% or more of the sampled mussels will be infected, using the normal approximation without the continuity correction.
B) Find the probability that 85% or more of the sampled mussels will be infected, using the the normal approximation with the continuity correction

Explanation / Answer

n=100, p=0.8 ----------------------------------------------------------------------------------------- (a) without the continuity correction: P(p > 0.85) = P[z > (0.85 - 0.8)/sqrt(0.8*0.2/100)] = P(z > 1.25) = 0.1056 (check standard normal table) ------------------------------------------------------------------------------------------------------------ (b) with the continuity correction: P(p > 0.845) = P[z > (0.845 - 0.8)/sqrt(0.8*0.2/100)] = P(z > 1.125) = 0.1303(check standard normal table)

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