Question

According to a recent​ study, some experts believe that 15​% 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 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 0.15. 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 37.5​, and n times​ (1 minus​ p) is 212.5​, and both are more than 10.

Answer 1

Sample proportion of fishes having high levels of mercury approximately follows Normal distribution.

standard error =

proportion that is 2 standard error above 0.15 is 0.15+(2*0.0226)=0.1952

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 0.15 is