What is the probability of having exactly 38 boys among the

What is the probability of having: exactly 38 boys among the 75 births? Less than 37 boys among the 75 births? At least 36 boys among the 75 births?

Solution

n=75

p=0.5

a).

Mean = np = 37.5

Variance = np(1 - p) = 18.75

Standard deviation = 4.330

1). P( x=38) = 0.091

2). P( x < 37) = 0.409

3). P( x >=36) = 0.678

( Binomial calculator used to answer)