Question

suppose i flip a coin n=100 times and i obtain heads x=44 times. assuming the coin is fair, calculate P(x>44) using the normal approximation with continuity correction. x=44 significantly low

Answer 1

n = 100

P(heads), p = 0.5

q = 1 - 0.5 = 0.5

Normal approximation to binomial: P(X < A) = P(Z < (A - mean)/standard deviation)

Mean = np

= 100 x 0.5

= 50

Standard deviation =

=

= 5

P(X > 44) = 1 - P(X < 44.5) (with continuity correction)

= 1 - P(Z < (44.5 - 50)/5)

= 1 - P(Z < -1.1)

= 1 - 0.1357

= 0.8643

A value is significantly low if the probability of occurrence is less than 0.05. Here, P(X 44) = 0.1357, which is greater than 0.05. Therefore, X = 44 is not significantly low.