In a certain population, the probability that a newborn child will be female is
ID: 2960218 • Letter: I
Question
In a certain population, the probability that a newborn child will be female is 0.55What is the probability that in a sample of 1000 births in this population, exactly 560 of them will be females?
I tried doing this 2 ways:
Method #1: 1000C560 * 0.55^560 * 0.45^440
I could not do it this way because my calculator would not allow it
Method #2: Using the Poisson formula: (550^560 * e^-550) / 560!
This, too, my calculator would not accept.
So how am I supposed to solve this problem? I know the answer is supposed to be 0.0229
I just don’t see how I can get there with a pocket calculator.
Thank you
Explanation / Answer
Given X~Binomial(n=1000, p=0.55)
By using Normal distribution approximation,
X~Normal(=n*p=1000*0.55= 550, s=n*p*(1-p) =sqrt(1000*0.55*(1-0.55))= 15.73)
So the probability is
P(X=560)= P(559.5 <X< 560.5) (By using continuous correction)
= P((559.5-550)/15.73 <(X-)/s < (560.5-550)/15.73)
=P(0.6<Z < 0.67 )
= 0.0228