Suppose that a quiz consists of 20 True-False questions. A student hasn't studied for the exam and will just randomly guesses at all answers (with True and False equally likely). How would you find the probability that the will student get 8 or fewer answers correct?
A) Find the probability that X = 8 in a binomial distribution with n = 20 and p = 0.5.
B) Find the area between 0 and 8 in a uniform distribution that goes from 0 to 20.
C) Find the probability that X = 8 for a normal distribution with mean of 10 and standard deviation of$\sqrt{5} $ .
D) Find the cumulative probability for 8 in a binomial distribution with n = 20 and p = 0.5.

Question

Quizplus · Accepted Answer

The correct approach is to use a binomial distribution because the scenario involves a fixed number of independent trials (20 True-False questions), each with two possible outcomes (True or False), and the probability of success (guessing correctly) is constant (0.5). The cumulative probability for getting 8 or fewer correct answers involves summing the probabilities of getting 0, 1, 2, ..., 8 correct answers, which is what option D suggests.

Suppose That a Quiz Consists of 20 True-False Questions 5\sqrt{5} 5​

Suppose That a Quiz Consists of 20 True-False Questions $\sqrt{5}$