according to an article from huffingtonpost.com, some experts believe that 20% of all freshwater fish in the united states have such high levels of mercury that they are dangerous to eat. suppose a fish market has 250 fish we consider randomly sampled from the population of edible freshwater fish. use the central limit theorem (and the empirical rule) to find the approximate probability that the market will have a proportion of fish with dangerously high levels of mercury that is more than two standard errors above 0.20. you can use the central limit theorem because the fish were randomly sampled; the population is more than 10 times 250; and n times p is 50, and n times (1 minus p) is 200, and both are more than 10.

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08-09-2022
Mathematics

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according to an article from huffingtonpost.com, some experts believe that 20% of all freshwater fish in the united states have such high levels of mercury that they are dangerous to eat. suppose a fish market has 250 fish we consider randomly sampled from the population of edible freshwater fish. use the central limit theorem (and the empirical rule) to find the approximate probability that the market will have a proportion of fish with dangerously high levels of mercury that is more than two standard errors above 0.20. you can use the central limit theorem because the fish were randomly sampled; the population is more than 10 times 250; and n times p is 50, and n times (1 minus p) is 200, and both are more than 10.

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Tutorconsortium219 Tutorconsortium219 · Answer 1 · 2022-09-13T07:36:03+02:00

Details given,

[tex]p=\mathbf{0.20},\;n=\mathbf{250}\\np=250*0.20=50\geq 10\\n(1-p \right )=250*0.80=200\geq 10\\[/tex]

In this instance, np and n(1-p) both exceed 10. Therefore, it can be said that the chosen sample is substantial.

[tex]Mean\;(\mu_{\hat p})=\hat p=\mathbf{{\ 0.20}}\\\\Standard \;error\;(\sigma_{\hat p})=\sqrt{\frac{ p*(1- p)}{n}}=\sqrt{\frac{0.20*0.80}{250}}=\mathbf{{\ 0.0253}}\\\\P(more\;than\;0.25)\Rightarrow P(\hat p > 0.25)\\\\P(\hat p > 0.25)\Rightarrow P\left (\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}} > \frac{0.25-0.20}{\sqrt{\frac{0.20*0.80}{250}}} \right )\\\\=P(Z > 1.98)[/tex]

= 0.0239

Therefore, there is a 0.0239 percent chance that some of the fish on the market will have dangerously high mercury levels.

What does probability mean in its entirety?

Simply put, probability is the likelihood that something will occur. Calculating a result or the likelihood that an event would ever occur is known as simple probability. Probability statistics are used by insurance firms to calculate the likelihood of having to pay out a claim. By dividing one possible outcome by all other possible possibilities, one can determine a basic probability.

Everyday existence heavily relies on probability. In the analysis of political strategies, the determination of blood types, sports and gaming strategies, purchasing or selling insurance, online shopping, and online games.

To learn more about probability, visit:

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