2b) Use the formulas for the mean and the standard deviation of a binomial random variable to calculate the mean and the standard deviation of X. ( round answer to the nearest thousandths) 2c) suppose a passing grade is 60%, which is three or more correct answers out of the five questions. What is the probability of passing the test? ( round to the nearest thousandth) 2d) what is the probability of scoring under 80% , meaning answering fewer than four questions correctly? ( round to the nearest thousandth) 2e) what is the probability that you to achieve a perfect score without studying for this test ? ( round to the nearest thousandth)

1. Consider a multiple-choice test with five questions, each with four possible choices. As is usually the case, there is only one correct answer for each question (meaning that there are three incorrect answers for each question). Unfortunately, you didn't study for this test, so you must resort to randomly guessing on each question. Let the discrete random variable X represent the number of questions you answer correctly. Consider this multiple-choice test as an experiment and consider each question as a Bernoulli trial. Explain how this situation satisfies all three conditions of Bernoulli trials. 2. Consider a multiple-choice test with five questions, each with four possible choices. As is usually the case, there is only one correct answer for each question (meaning that there are three incorrect answers for each question). Unfortunately, you didn't study for this test, so you must resort to randomly guessing on each question. Let the discrete random variable X represent the number of questions you answer correctly. Use the binomial probability formula to fill in the following table of the probability distribution of X. (Round each answer to the nearest thousandth.) Correct Answers x Probability P(X = x) O 2 W 4 5