Question

Next, determine the probability of getting an obscure ratio or worse. That is: (a)What is the probability of having 33% boys or less? (in 1000 births, 330 would be male) (b)What is the probability of having 41% boys or less? (in 1000 births,410 would be male) (c)What is the probability of having 1200 boys for every 1000 girls or 54.5% boys? (in 1000 births, 545 would be male)

Answer 1

The number of boys in 1000 births is modelled here as:

Approximating it to a normal distribution, we have here:

a) The probability of having 330 or less males is computed here as:
P(X <= 330)

Applying the continuity correction, we have here:
P(X < 330.5)

Converting it to a standard normal variable, we have here:

Getting it from the standard normal tables, we have here:

Therefore 0 is the required probability here.

b) Similar to above part, the probability here is computed as:

Getting it from the standard normal tables, we have here:

Therefore 0 is the required probability here.

c) The probability of having 1200 boys for every 1000 girls or 54.5% boys is computed here as:

P(X = 1200 boys in 2200 children)

Therefore 0.0000019 is the required probability here.