In a certain population of mussels (Mytilus edulis) 80% of the individuals are i

Question

In a certain population of mussels (Mytilus edulis) 80% of the individuals are infected with an intestinal parasite. A marine biologist plans o examine 100 randomly chosen mussels from the population. Find the probability that 85% or more of the sampled mussels will be infected, using the normal approximation without the continuity correction. Refer to Exercise 5.4.12. Find the probability that 85% or more of the sampled mussels will be infected, using the normal approximation with the continuity correction. Refer to Exercise 5.4.12. Suppose that the biologist takes a random sample of size 50. Find the probability that fewer than 35 of the sampled mussels will be infect, using the normal approximation without the continuity correction. with the continuity correction.

Explanation / Answer

5.4.12

p=0.80

n=100

standard error = sqrt(pq/n) =sqrt(0.8*0.2/100) =0.04

z value for 0.85, z=(0.85-0.80)/0.04 =1.25

P( p0.85)

=P( z >1.25)

= 0.1056

5.4.13

With continuity correction

z value for 0.85, z=(0.845-0.80)/0.04 =1.125

P( p0.85)

=P( z >1.125)

= 0.1303

5.4.14

p=0.80

n=50

standard error = sqrt(pq/n) =sqrt(0.8*0.2/50) =0.0566

35 is 70%

z value for 0.70, z=(0.70-0.80)/0.0566 =-1.77

P( p<0.70)

=P( z < -1.77)

= 0.0384

With continuity correction

z value for 0.70, z=(0.695-0.80)/0.0566 =-1.86

P( p 0.70)

=P( z < -1.86)

= 0.0314

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---