Mathematics, 15.04.2020 22:38 ciaralamont2

In a certain population of mussels (Mytilus 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 normal approximation to binomial distribution.

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Answer from: randyg0531

The probability that 85% or more of the sampled mussels will be infected is 0.1057.

Step-by-step explanation:

Let X = number of mussels infected with an intestinal parasite.

The probability that a random selected mussel is infected with an intestinal parasite is, p = 0.80.

A random sample of n = 100 mussels from the population are examined by a marine biologist.

The random variable X follows a Binomial distribution with parameters n = 100 and p = 0.80.

But the sample selected is too large, i.e. n = 100 > 30.

So a Normal approximation to binomial can be applied to approximate the distribution of $\hat p$ , the sample proportion of mussels infected with an intestinal parasite, if the following conditions are satisfied:

np ≥ 10 n(1 - p) ≥ 10

Check the conditions as follows:

n × p = 100 × 0.80 = 80 > 10

n × (1 - p) = 100 × (1 - 0.80) = 20 > 10

Thus, a Normal approximation to binomial can be applied.

So, the distribution of $\hat p$ is:

$\hat p\sim N(p, \frac{p(1-p)}{n} )$

Compute the probability that 85% or more of the sampled mussels will be infected as follows:

Apply continuity correction:

$P(\hat p\geq 0.85)=P(\hat p0.85+0.50)$

$=P(\hat p0.90)\\$

$=P(\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}\frac{0.85-0.80}{\sqrt{\frac{0.80(1-0.80)}{100}}})$

$=P(Z1.25)\\=1-P(Z$

*Use a z-table for the probability.

Thus, the probability that 85% or more of the sampled mussels will be infected is 0.1057.

Answer from: Quest

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.

Answer from: Quest

step-by-step explanation:

to find if any function is an inverse of the other, put the first equation in as x in the next one. then simplify and solve. if at the end you get the statement y = x, then it is an inverse. if you get anything else, it is not.

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