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 halloweengrl23 March 21st, 2012 10:16 PM

Probability problem

Can someone please help me out with this problem, i would appreciate it a a lot!

Based upon statistical studies it has been found that 0.18% of all births in the United States will result in triplets being born. If 26,900 births are selected at random what is the probability that

a) at least 40 of them will result in triplets being born?
b) between 25 and 50 of them will result in triplets being born?

 Erimess March 21st, 2012 10:54 PM

Re: Probability problem

If this were just a sample of x's instead of a proportion, could you do it? Cause it's not terribly much different.

Instead of $\sigma_{\overline{x}}\=\ \frac{\sigma}{sqrt{n}}$ (standard error of sample mean)

You have $\sigma_{\overline{p}}\=\ sqrt{\frac{p(1\ -\ p)}{n}}$ (standard error of a sample proportion)

Your p = .0018

When you go to figure the probabilities, you have to convert the numbers to p's. Hence, 40/26900 would give you the p number you need, and you calculate the probability of it being bigger than that, etc. Just use the z equation like normal:

$z\=\ \frac{x\ -\ \mu}{\sigma}$ (population)

$z\=\ \frac{\overline{x}\ -\ \mu}{\sigma_{\overline{x}}}$ (sample mean)

$z\=\ \frac{\overline{p}\ -\ p}{\sigma_{\overline{p}}}$ (sample proportion)

If you take a good look at them, they're all essentially the same: point minus its mean, divided by its standard deviation. It just has to be relative to whatever point you're using.

Can you go from here?

 halloweengrl23 March 22nd, 2012 04:56 PM

Re: Probability problem

Ok so I tried it out and here are the answers that I got:

A) .8871
B) .5895

Are those right?

 Erimess March 23rd, 2012 02:27 AM

Re: Probability problem

The first one I got .8869, but I'm fairly sure that's just rounding.

This proves to me that you're getting the basic idea, but the second one is way, way off. Since the equations would all be the same, I suspect it's in figuring out what portion of the distribution (graph) you would be using. The 50 (~.0018587) would be to the right of the .0018. The 25 (~.0009294) is way far to the left. Best way to figure that is figuring everything to the left of the first one, and then subtracting everything to the left of the second.

That is, let's saying you were looking for something between 2 and 7. Think of a number line. Everything to the left of 7 is, well, 7. And then you'd want to subtract off everything to the left of 2, which is 2. That leaves you 5 in between those. If that makes sense. (Hard to describe, but also a pain to try to draw and get the image on here.)

The only thing is, everything to the left of .0009294 is essentially about nothing, so in the end there isn't really anything to subtract off.

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