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Normal approximation

Hello,

I've been stuck on the second part of this particular question: ImageUploadedByStudent Room1464538163.559274.jpg

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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Original post by nemanuel96
Hello,

I've been stuck on the second part of this particular question: ImageUploadedByStudent Room1464538163.559274.jpg

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.
Reply 2
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nemanuel96
OP
10
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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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.
(edited 7 years ago)
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
Reply 5
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nemanuel96
OP
10
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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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:

50C25(0.55)25(0.45)25^{50}C_{25}(0.55)^{25}(0.45)^{25}
Reply 7
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nemanuel96
OP
10
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:

50C25(0.55)25(0.45)25^{50}C_{25}(0.55)^{25}(0.45)^{25}


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


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Reply 8
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nemanuel96
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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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Reply 9
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nemanuel96
OP
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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Thank you both very much. I've had a look over it and it makes a lot of sense!


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