Question

The number of heads in 100 flips of a fair coin is approximately Normally distributed. To estimate the chance of getting between 49 and 51 heads (inclusive), what would the endpoints of the interval be after a continuity correction?

Answer 1

X ~ Bin ( n , p)

Where n = 100 , p = 0.50

Mean = n p = 100 * 0.50 = 50

Standard deviation = sqrt [ n p ( 1 - p) ] = sqrt [ 100 * 0.5 * 0.5 ] = 5

Using normal approximation,

P(X < x) = P(Z < ( x - mean) / SD )

With continuity correction,

P(49 X 51) = P(48.5 < X < 51.5)

P ( 48.5 < X < 51.5 ) = P ( Z < ( 51.5 - 50 ) / 5 ) - P ( Z < ( 48.5 - 50 ) / 5 )

= P ( Z < 0.3) - P ( Z < -0.3 )

= 0.6179 - 0.3821 (From Z table)

= 0.2358