Question

In Chelmsford County, the probability that a randomly chosen birth results in a boy is 45% at the local hospital. Over the course of a month, there are 20 births.

c. Use the binomial probability formula to calculate the probability that more than 14 boys are born in these 20 births.

Can you show the full steps for this question including how to find the probability for each possible outcome?

Answer 1

Answer in detail with steps as asked in the question. I 've also put down the formula to solve the problem and the concept. Let me know in case you've not understood any part of it.

2nd part of the question: Each outcome can be calulcated as :

P(x,n,p) = Probability of x occurences out of n total trials , with the probability of event happening is p

So, for example:

P(3 out of 20 biths result in boy )

= P(3,20,.45)

= nCx(p^x)*(1-p)^(n-x)

= 20C3 * .45^3 * .55^17

= 0.04006

Part (c)

Now, lets calculate (c)

In (c) we have to calculate P(X>14)

= P(X=15,16,17,18,19,20)

= 20C15*.45^15*.55^5 + 20C16*.45^16*.55^4+20C17*.45^17*.55^3+20C18*.45^18*.55^2+20C19*.45^19*.55^1

+ 20C20*.45^20*.55^0

= 0.006434

ANSWER : 0.006434