Please explain the steps so I can better understand. Thank you

1. A multiple choice test has 10 questions, and each question has 5 answer choices (exactly one of which is correct). A student taking the test guesses randomly on all questions. Find the probability that the student will actually get at least as many correct answers as she would expect to get with the random guessing approach. (Please explain your solution) 2. The probability that a particular machine breaks down in any day is .20 and is inde- pendent of the breakdowns on any other day. The machine can break down only once per day. Calculate the probability that the machine breaks down two or more times in ten days. (Please explain your solution) 3. If for a certain normal random variable X, P[X - 500] =.5 and PX >> 650 = .0227, find the standard deviation of X. (Please explain your solution) 4. A study is being conducted in which the health of two independent groups of ten poli- cyholders is being monitored over a one-year period of time. Individual participants in the study drop out before the end of the study with probability 0.2 (independently of the other participants). What is the probability that at least 9 participants complete the study in one of the two groups, but not in both groups? (Please explain your solution)