A coin is tossed 100 times and the results are recorded. 40 times the coin lands on heads, the other 60 times the coin lands on tails. If 40 of the recorded tosses were selected at random, what is the probability that the coin landed on heads exactly 14 times?
P(head ) = 40 / 100 = 0.40 , P(Tail) = 60 / 100 = 0.60
X ~ bin ( n , p)
Where n = 40 , p = 0.40
Using Normal Approximation to Binomial
Mean = n * P = ( 40 * 0.4 ) = 16
Variance = n * P * Q = ( 40 * 0.4 * 0.6 ) = 9.6
Standard deviation = √(variance) = √(9.6) =
3.0984
Using continuity correction
P(X = 14) = P(13.5 < X < 14.5)
P ( 13.5 < X < 14.5 ) = P ( Z < ( 14.5 - 16 ) / 3.0984
) - P ( Z < ( 13.5 - 16 ) / 3.0984 )
= P ( Z < -0.48) - P ( Z < -0.81 )
= 0.3156 - 0.209
= 0.1066
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