A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped 2828 times, and the man is asked to predict the outcome in advance. He gets 2121 out of 2828 correct. What is the probability that he would have done at least this well if he had no ESP?
Number of flips, n = 28
P(correct answer if he had no ESP), p = 0.5
q = 1 - 0.5 = 0.5
np = 28x0.5 = 14
nq = 28x0.5 = 14
np and nq > 5
Therefore, normal approximation to binomial can be used.
P(X < A) = P(Z < (A - mean)/standard deviation)
Mean = np = 14
Standard deviation =
=
= 2.646
P(he would have done at least this well if he had no ESP) = P(X 21)
= 1 - P(X < 20.5) (with continuity correction)
= 1 - P(Z < (20.5 - 14)/2.646)
= 1 - P(Z < 2.46)
= 1 - 0.9931
= 0.0069
Get Answers For Free
Most questions answered within 1 hours.