According to the manufacturer of the candy Skittles, 25% of the candy produced are green. If we take a random sample of 10 bags of Skittles, what is the probability that the proportion in our sample of green candies will be more than 25%? Which statement, if any, is true for the conditions to use the Central Limit Theorem?
A)The success/failure conditions may not be satisfied.
B)The sample size is small compared to the population.
C)Though not from a random sample, we can assume that the bags are representative of the population.
D)All of these statements are not true.

Question

Quizplus · Accepted Answer

DA) The success/failure condition for the Central Limit Theorem (CLT) requires that the sample size be large enough so that both the expected number of successes (np) and failures (n(1-p)) are greater than or equal to 10. With a probability of 25% for green candies, and a sample size of 10 bags, we might not always meet this condition, especially if we interpret "success" as selecting a green candy. D) The statement that all of these statements are not true is correct because the conditions for the CLT do involve considerations about sample size and randomness. The sample size being small compared to the population is generally not a concern for the CLT; the focus is on the sample size being sufficiently large to approximate the sampling distribution of the sample proportion as normal. The assumption that bags are representative of the population is crucial for any inference and is aligned with the requirement for a random sample, which is a condition for applying the CLT.

According to the Manufacturer of the Candy Skittles, 25% of the Candy