Suppose that Illinois lawmakers survey 130 randomly selected registered voters to see if they favorcharging a deposit on aluminum cans to encourage recycling. The lawmakers believe thepopulation proportion in favor of changing the law is 93% (based on historical data and previousvotes). Which of the following conditions for the Central Limit theorem arenotmet?
A)Relative to the population, the sample is not large enough.
B)The population proportion is too small and will not have enough expected successes.
C)The population proportion is too small and will not have enough expected failures.
D)None of these, all the conditions of the CLT are met.

Question

Quizplus · Accepted Answer

The condition for the Central Limit Theorem requires that both np and n(1-p) be greater than 5. Here, n(1-p) = 130 * 0.07 = 9.1, which is greater than 5, so the condition is met.

Suppose That Illinois Lawmakers Survey 130 Randomly Selected Registered Voters