i. As a general rule of thumb, if the items selected for a sample are not replaced and the sample size is less than 5 percent of the population, the binomial distribution can be used to approximate the hypergeometric distribution. ii. If the probability of success does not remain the same from trial to trial when sampling is done without replacement, the hypergeometric distribution should be applied.
iii. In the hypergeometric distribution the probability of a success is not the same on each trail.
A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question

Quizplus · Accepted Answer

All three statements are correct. Statement (i) is true because when the sample size is small relative to the population (less than 5%), the difference between binomial and hypergeometric distributions is negligible, allowing the binomial distribution to approximate the hypergeometric distribution. Statement (ii) correctly identifies a scenario where the hypergeometric distribution is appropriate, as it accounts for changing probabilities of success when sampling without replacement. Statement (iii) accurately describes a characteristic of the hypergeometric distribution, where the probability of success changes with each draw since the composition of the population changes with each selection.

I as a General Rule of Thumb, If the Items