Normal approximation to binomial

[JellyFish]

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

 

[royhaas]

Set up the inequality that represents the normal approximation and solve for the sample size.

 

[JellyFish]

I have that E(x) = 0.65n = ?

and that ? = sqr(0.2275n)

I think I want to solve for n the sample space?

I am not sure where to go form here as I don't know where the at least 6 and 80% come in.

Thanks again

 

[galactus]

Look up the z score that corresponds to .80. That is about .8415. Since we want 'at least 6', then use 1-.8415=.1585

The binomial continuity correction for at least 6 would be 5.5

\(\displaystyle .1585=\frac{5.5-.65n}{\sqrt{.2275n}}\)

solve for n.

That seems to be the way to go about it.

 

[JellyFish]

Thank you, I tried that way and it seemed to work out.


Thank you again for your help