According to a recent study, some experts believe that 22.22 % of all freshwater fish in a particular country have such high levels of mercury that they are dangerous to eat. Suppose a fish market has 150 fish we consider randomly sampled from the population of edible freshwater fish.

Use Central Limit Theorem (and the Empirical rule) to find the approximate probability that the market will have a proportion of fish with dangerously high level of mercury that is more than two standard errors above 0.20.

You can use Central Limit Theorem because the fish were randomly sampled; the population is more than 10 times 250; and np is 50, and n (1-p) is 200, and both are more than 10.

Question

Hillary Oconnell

Mathematics

4 October, 16:23

According to a recent study, some experts believe that 22.22 % of all freshwater fish in a particular country have such high levels of mercury that they are dangerous to eat. Suppose a fish market has 150 fish we consider randomly sampled from the population of edible freshwater fish.

Use Central Limit Theorem (and the Empirical rule) to find the approximate probability that the market will have a proportion of fish with dangerously high level of mercury that is more than two standard errors above 0.20.

You can use Central Limit Theorem because the fish were randomly sampled; the population is more than 10 times 250; and np is 50, and n (1-p) is 200, and both are more than 10.

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Omar · Answer 1

Step-by-step explanation:

Given that according to a recent study, some experts believe that 22.22 % of all freshwater fish in a particular country have such high levels of mercury that they are dangerous to eat.

Here number of fish n = 150

Sampling method = random

Outcomes = only two whether dangerous or not dangerous

Each fish is independent of the other

Hence No of fish that is dangerous is binomial with n = 150 and p = 0.2222

np >10 and n (1-p) >10

Hence binomial approximation can be applied