Question

In a test for ESP (extrasensory perception) the experimenter looks at cards that are hidden from the subject. The experimenter looks at many cards bearing one of five shapes (star, square, circle, wave and cross) in an order determined by random numbers. The subject cannot see the experimenter as he looks at each card in turn, in order to avoid any possible non verbal clues. We can consider the population to be an infinite number of guesses where the trait is a correct guess, Therefor, 1000 attempts can be considered a sample because it is a subset of the population of an infinite number of guesses. Moreover the answer of a subject has a probability 1/5 of success, the proportion of an infinite number of guesses is considered to be 1 out of 5.

What are the mean and standard deviation of the proportion of successes among 1000 attempts?

Answer 1