Joe performs remarkably well on remote viewing ESP tests, which require the "viewer" to draw a picture, then determine which of four possible photos was the intended "target". Because the target is randomly selected from among the four choices, the probability of a correct match by chance is 1/4, or 0.25. Joe participates in three experiments with n = 10, 30, and 40 trials, respectively. In the three experiments, his numbers correct are 2, 6, and 8, respectively, for a total of 16 correct out of 80 trials.

(a) For each experiment, what is the expected number correct if Joe is just guessing?

forn=10 the mean = forn=30 the mean = forn=40 the mean =

(b) Over all 80 trials, what is the expected number correct, ? =

(c) For each experiment separately, find the approximate probability, P that someone would get as many correct as Joe did, or more, if the person was just guessing. (Use the binomial distribution. Round all answers to four decimal places.)

forn=10 P(x2) = forn=30 P(x6) = forn=40 P(x8) =

(d) Out of the 80 trials overall, find the approximate probability that someone would get as many correct as Joe did (16), or more, if the person was just guessing. (Use the binomial distribution. Round the answer to four decimal places.) P(x 16) =