Question

You have a coin that is not weighted evenly and therefore is not a fair coin. Assume the true probability of getting heads when the coin is flipped is 0.52 Find the probability that less than 76 out of  157 flips of the coin are heads.

Answer 1

P(heads), p = 0.52

q = 1 - p = 0.48

Number of flips, n = 157

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

Mean = np

= 157x0.52

= 81.64

Standard deviation =

=

= 6.26

P(less than 76 out of 157 flips of the coin are heads) = P(X < 76)

= P(X < 75.5) (after applying continuity correction of 0.5)

= P(Z < (75.5 - 81.64)/6.26)

= P(Z < -0.98)

= 0.1635