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# Normal approximation watch

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.

Posted from TSR Mobile
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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