i. For a binomial distribution, each trial has a known number of successes. For example, a four question multiple-choice test can only have zero, one, two, three and four successes (number correct). ii. To construct a binomial probability distribution, the number of trials and the probability of success must be known.
iii. A binomial distribution has a characteristic that the trials are independent, which means that the outcome of one trial does not affect the outcome of any other trial.
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. The binomial distribution is characterized by a fixed number of independent trials, each trial having only two outcomes (success or failure), and a fixed probability of success for each trial. The number of possible successes is also fixed, as stated in statement (i). The probability distribution for this scenario must be constructed by knowing both the number of trials and the probability of success, as stated in statement (ii). Finally, the independence of the trials means that the outcome of one trial does not affect any other trial, as stated in statement (iii).

I for a Binomial Distribution, Each Trial Has a Known