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# Normal approximation

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1. Hello,

I've been stuck on the second part of this particular question:

I've managed to do the first part but I'm finding the last part a little tricky. I don't understand what I'd use for the mean once I've approximated it or the X.

Thanks, any help would be greatly appreciated.

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2. (Original post by nemanuel96)
Hello,

I've been stuck on the second part of this particular question:

I've managed to do the first part but I'm finding the last part a little tricky. I don't understand what I'd use for the mean once I've approximated it or the X.

Thanks, any help would be greatly appreciated.

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It's the same sample as before, so the same distribution.
3. (Original post by ghostwalker)
It's the same sample as before, so the same distribution.
I still don't really understand so would it:

Z = (27.5 - 22.5)/√12.375

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4. (Original post by nemanuel96)
I still don't really understand so would it:

Z = (27.5 - 22.5)/√12.375

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I can't make sense of that - please elaborate and explain what you're doing there.

I can see you've used np(1-p) to get the variance, and thus s.d. of root(12.375), but don't follow what you're doing with the top bit.
5. (Original post by nemanuel96)
I still don't really understand so would it:

Z = (27.5 - 22.5)/√12.375

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I think you want to find the probability of 25 Republicans (both equal) so P(X=25) which would be P(24.5<y<25.5) for normal approximation or you could use the formula
6. (Original post by ghostwalker)
I can't make sense of that - please elaborate and explain what you're doing there.

I can see you've used np(1-p) to get the variance, and thus s.d. of root(12.375), but don't follow what you're doing with the top bit.
Sorry, you're right. I've used M(np) =(50*0.55) = 27.5

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7. (Original post by nemanuel96)
Sorry, you're right. I've used M(np) =(50*0.55) = 27.5

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OK, but still puzzled where the 22.5 came from then - looks to be 50*0.45.

Anyhow, you're looking for the probability of the number of Republicans and Monarchists being equal. And in a sample of 50, that's 25 of each.

As SugarCoatedCart said, P(X=25) which allowing for the continuity correction is P(24.5<x<25.5)

So, you're going to need to work out the Z value for 25.5, and it's cumulative probability, and similarly for 24.5.

Subtracting one from the other will give you P(24.5<x<25.5), your desired result.

Note that this could be done with the binomial directly if your calculator would allow it: Find P(X=25) where X~B(50,0.55), which is:

8. (Original post by ghostwalker)
OK, but still puzzled where the 22.5 came from then - looks to be 50*0.45.

Anyhow, you're looking for the probability of the number of Republicans and Monarchists being equal. And in a sample of 50, that's 25 of each.

As SugarCoatedCart said, P(X=25) which allowing for the continuity correction is P(24.5<x<25.5)

So, you're going to need to work out the Z value for 25.5, and it's cumulative probability, and similarly for 24.5.

Subtracting one from the other will give you P(24.5<x<25.5), your desired result.

Note that this could be done with the binomial directly if your calculator would allow it: Find P(X=25) where X~B(50,0.55), which is:

0.45 x 50 = 22.5. I apologise for the confusion, I'm very tired.

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9. (Original post by nemanuel96)
0.45 x 50 = 22.5. I apologise for the confusion, I'm very tired.

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For the Republicans mind you.

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10. Thank you both for your input, it's greatly appreciated.

Going to get some sleep and look over it tomorrow.

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11. Thank you both very much. I've had a look over it and it makes a lot of sense!

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