# Normal approximation to binomial

• Jul 29th 2009, 01:04 PM
CoraGB
Normal approximation to binomial
In the following question I know that I am supposed to use the normal approximation to the binomial which we have covered in class but I am not sure how to apply it here.

It has been statistically determined that 65% of the new chicks of a bird can survive winter. What is the minimum number of chicks to hatch before winter such that there is a 80% probability that at least 6 will survive.

Thank you
• Jul 29th 2009, 07:47 PM
mr fantastic
Quote:

Originally Posted by CoraGB
In the following question I know that I am supposed to use the normal approximation to the binomial which we have covered in class but I am not sure how to apply it here.

It has been statistically determined that 65% of the new chicks of a bird can survive winter. What is the minimum number of chicks to hatch before winter such that there is a 80% probability that at least 6 will survive.

Thank you

Start by defining your random variable: Let X be the random variable number of chicks that survive hatching.

Define the distribution followed by X: X ~ Binomial(n = ?, p = 0.65).

Write a probability statement that encapsulates the question: Find the minimum value of n such that $\displaystyle \Pr(X \geq 6) \geq 0.8$.

Using trial and error (or, even better, technology) it doesn't take long to get n = 11. I don't see why the normal approximation would be required here.
• Jul 29th 2009, 08:06 PM
VonNemo19
Thank you Mr. F for your insight into this difficult topic. You are indeed a fine gentelman, and you have helped me a great deal. I'm off to the bus now. I'm very late...

Regards.
• Jul 29th 2009, 11:05 PM
CaptainBlack
Quote:

Originally Posted by CoraGB
In the following question I know that I am supposed to use the normal approximation to the binomial which we have covered in class but I am not sure how to apply it here.

It has been statistically determined that 65% of the new chicks of a bird can survive winter. What is the minimum number of chicks to hatch before winter such that there is a 80% probability that at least 6 will survive.

Thank you

Suppose that $\displaystyle N$ chicks hatch, the number that survive $\displaystyle \sim B(N,0.65)$ , you are asked to find the smallest $\displaystyle N$ so that $\displaystyle p(n\ge 6)\ge 0.8$ where $\displaystyle p(n\ge 6)$ is that probability that there are $\displaystyle 6$ or more survivours.

Using the normal approximation the number of survivours is to be treated as a normal random variable with mean $\displaystyle 0.65N$ and SD $\displaystyle \sqrt{N\times0.65\times0.35}$.

CB