In-Class Activity 8.C, we defined a binomial experiment as an experiment consisting of a fixed number, n , of independent Bernoulli trials that count the number of successes out of n trials. Notice that the number of successes in a binomial experiment is a discrete random variable. The distribution of this random variable is modeled with the binomial distribution. Binomial Distribution For a binomial experiment, the mean and standard deviation are defined as follows: The mean of the number of successes is = n p . The standard deviation of the number of successes is = n p ( 1 p ) . Common tests such as the SAT, ACT, LSAT, and MCAT use multiple-choice test questions with five possible answer choices (a, b, c, d, and e). In addition, each question has only one correct answer. Part A: Let the random variable X represent the number of correct responses. For people who make random guesses for answers to a block of 100 questions, identify the values for p , 1 p , mean of X , and standard deviation of X . p = 1 p = X =