# Thread: Normal approximation to binomial

1. ## 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

2. 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 $\Pr(X \geq 6) \geq 0.8$.

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.

3. 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.

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

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

CB