math

An ESP study discovers a subject whose performance appears to be better than guessing. 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 to avoid any nonverbal clues. The answers of a non-ESP subject should be independent observations, each with probability 1/5 of success. We record 1000 samples. What are the mean and standard deviation of the proportion of successes among the 1000 attempts?

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  1. The mean should be (1/5)*1000 = 200 correct guesses and the standard deviation should be
    sqrt [p(1-p)N] = sqrt[(1/5)(4/5)1000] = 12.65

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