Statistics Problem

1. Bill has completed a ten question multiple choice test on which he answered seven questions correctly.  Each question had one correct answer to be chosen from four alternatives.  Bill says that he answered the test by randomly selecting the answers without reading the questions or answers.

a. What is the expected number of correct responses under these circumstances if one in fact selects the responses at random.  What is the standard deviation?
b. What is the probability of Bill guessing seven of the ten answers correctly?
c. What is the probability that one could guess six or more answers correctly?
d. What do you think of Bill’s claim?  Explain.