Re: Stats; On Continuity Correction, need to know when to + or - 0.5?

Question

thank goodness for add details:

I basically need to know that when P(x is something to n) I need to know when to add or subtract 0.5 to n

I have read different sites and still do not see a full or elementary explanation of this. So if possible, please answer these probably easy questions:
But for my comprehension, please answer this way
Example: P(x>n) : +0.5 Meaning that N must change its value in P(x>n) to P(x>n+0.5)
Thank you ahead of time, it is highly appreciated!
If need be, n=5
low#n = 2 high# n = 5


P(x>n) :
P(x>=n) :
P(x P(x<=n) :
P(low# n < x < high# n) :
P(low#n <= x , <= high#n) :
P(x=n) :

Answer 1

when you use continuity correction, you just have to imagine the normal curve and imagine it being divided into bars or strips (a bit like the trapezium rule). therefore, when you refer to the bar corresponding to say, 4, on the 'x-axis', the 4 goes up the centre of the bar and is flanked on both sides by its limits: (4-0.5=3.5) and (4+0.5=4.5).

Now when we say <4, in continuity correction, we mean to say <3.5 because the 4 must be considered as the ' bar of 4 ', meaning that you have to consider the lower limit too (3.5) [we want less than 4, menaing less than anything than has to do with 4, thus, less than its lower limit]

when we say <=4, the '=' means we are including the 4 and anything that has to do with it: hence, the upper limit of the 'bar of 4' , 4.5 has to be included too.

therefore,

for n=4,

P(x>4) ----> P(x>4.5)
P(x>=4) ----> P(x>3.5)
P(x<4) -------> P(x<3.5)
P(x<=4) ------> P(x<4.5)
P(2 break this down into: P(x>2) and P(x<5)
---------> P(2.5
P(2<=x<=5) -------> P(1.5 P(x=4) -----> remember the bar mentioned above, with its limits
-----> P(3.5
(hope i've not confused u even more) :-)

Answer 2

interior the binomial threat distribution each random variable has barriers of r - 0.5 and r + 0.5 for the continuity correction component. a. considering the fact which you're observing values to the best of 40 4 and mutually with 40 4, use the cost 40 3.5 to comprise the rectangle interior the section under the traditional curve b. you desire are to the left yet no longer mutually with 31, so flow to the left of 31 by capacity of subtracting 0.5 --> 30.5