A student takes a multiple choice exam with 10 questions, each with 5 possible selections for the answer. Suppose that the student was unable to find time to study for the exam and just guesses at each question. Find the probability that the student:
a. Gets at least one question correct.
b. Passes the exam (60% or better).
c. Receives an "A" on the exam (90% or better).
d. How many questions would you expect the student to get correct?
e. Obtain the standard deviation of the number of questions that the student gets correct.