In a certain population of mussels, 80% of the individuals are infected with an
ID: 3126843 • Letter: I
Question
In a certain population of mussels, 80% of the individuals are infected with an intestinal parasite. A marine biologist plans to examine 50 randomly chosen mussels from the population. Find the probability that fewer than 35 of the sampled mussels will be infected using the normal approximation (a) without 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)