Question

Use normal approximation (without continuity correction) to estimate the probability of getting at most 50 girls in 100 births. Assume that boys and girls are equally likely.

Answer 1

X ~ bin ( n , p)

Where n = 100 , p = 0.50 (Since boys and girls are equally likely)

Mean = n p = 100 * 0.50 = 50

Standard deviation sqrt [ n p ( 1 - p) ]

= sqrt [ 100 * 0.50 * 0.50 ]  

= 5

Using normal approximation,

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

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

= P(Z < 0)

= 0.50(From Z table)