# Normal approximation

• Nov 12th 2008, 11:10 PM
cechmanek32
Normal approximation
An orchard owner knows that he'll have to use about 8% of the apples he harvests for cider because they will have bruises or blemishes. He expects a tree to produce about 500 apples. Using the normal approximation to the binomial, find the probability the orchard owner will obtain at most 25 cider apples from the 500.

I think i know where to start: P(x< or equal to 25) but I am completely stuck beyond this point. I have looked at all the other models I have in regards to proportions and square roots of npq and I cannot figure this one out. Any help would be greatly appreciated. Thanks!
• Nov 13th 2008, 12:14 AM
mr fantastic
Quote:

Originally Posted by cechmanek32
An orchard owner knows that he'll have to use about 8% of the apples he harvests for cider because they will have bruises or blemishes. He expects a tree to produce about 500 apples. Using the normal approximation to the binomial, find the probability the orchard owner will obtain at most 25 cider apples from the 500.

I think i know where to start: P(x< or equal to 25) but I am completely stuck beyond this point. I have looked at all the other models I have in regards to proportions and square roots of npq and I cannot figure this one out. Any help would be greatly appreciated. Thanks!

Asked by another member here: http://www.mathhelpforum.com/math-he...-binomial.html

The approach is actually the same as the one I showed you here: http://www.mathhelpforum.com/math-he...t-theorem.html
• Nov 13th 2008, 10:18 AM
cechmanek32
Thanks for all the help but I think this is just a lost cause for me. I have no idea which of the numbers I found to plug in and where to plug them into the equation of (x<7). Thanks anyway for trying.
• Nov 13th 2008, 11:59 AM
mr fantastic
Quote:

Originally Posted by cechmanek32
Thanks for all the help but I think this is just a lost cause for me. I have no idea which of the numbers I found to plug in and where to plug them into the equation of (x<7). Thanks anyway for trying.

But can you answer the questions I asked!? State the normal approximation to the binomial distribution and state the conditions for its use to be valid.

Let X be the random variable number of bruised apples.

X ~ Binomial(n = 500, p = 0.08).

Calculate $\Pr(X \leq 25)$.

You can use the normal approximation to the binomial distribution.

Can you state this approximation?
Can you state why it can be used? (That is, what are the conditions that have to be met?)