Jones claims to have extrasensory perception (ESP). In order to test the claim, a psychologist shows Jones five cards that carry different pictures. Then Jones is blindfolded and the psychologist selects one card and asks Jones to identify the picture. This process is repeated 16 times. Suppose, in reality, that Jones has no ESP but responds by sheer guesses.
(a) What is the probability that the identifications are correct at most 8 times?
(b) What is the probability that the identifications are wrong at least 10 times?
(c) Find the expected value and standard deviation of the number of correct identifications.