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continuity correction Watch

1. Hello......I always confuse the rules of using continuity correction. On my textbook, P(X ≤ n)≈P(Y < n+0.5), P(X ≥ n)≈P(Y ≥ -0.5). And the example on the book, P( a ≤ X < b ) ≈ P( (a - 0.5) ≤ Y < (b + 0.5) )、 P( a ≤ X ≤ b ) ≈ P( (a - 0.5) ≤ Y ≤ (b + 0.5) )

But according the information that I found on the internet,

P( Xb < x) ≈ P( Xn < (x - 0.5) )
P( Xb > x) ≈ P( Xn > (x + 0.5) )
P( Xb ≤ x) ≈ P( Xn ≤ (x + 0.5) )
P( Xb ≥ x) ≈ P( Xn ≥ (x - 0.5) )
P( Xb = x) ≈ P( (x - 0.5) < Xn < (x + 0.5) )
P( a ≤ Xb ≤ b ) ≈ P( (a - 0.5) < Xn < (b + 0.5) )
P( a ≤ Xb < b ) ≈ P( (a - 0.5) < Xn < (b - 0.5) )
P( a < Xb ≤ b ) ≈ P( (a + 0.5) < Xn < (b + 0.5) )
P( a < Xb < b ) ≈ P( (a + 0.5) < Xn < (b - 0.5) )

There're some differences of the signs " < > ≤ ≥" between the textbook and the online information.

Can someone give me a hand? Thx~^^
2. A picture is worth a thousand words.
3. Thx for your help...but would you pls explan in more detail？
4. (Original post by ki_ki_ki)
Thx for you help...but would you pls explan in more detail？
Let's say X is discrete and Y is continuous and that Y can be used to approximate X.

If you need, for example to find P(X<20) then you need to consider two sets of numbers, everything and everything .

What number falls between those two sets?
5. Is 19.5?
6. (Original post by ki_ki_ki)
Is 19.5?
Yes.

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Updated: March 28, 2013
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