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Old 02-13-2019, 01:53 PM
masweeney718 masweeney718 is offline
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Default continuity correction

I'm using Actex to study for P. Taking the test next month.

Please give me a hand here. Continuity correction.....
so this is from the 3rd free exam on TIA. Why do we want P(Z>55.5) rather than P(Z>54.5)? I feel like I've gone through the book every time I do a continuity correction problems. I thought I'd finally understood it and now this comes up...

Based on Actex, I feel like if you are doing P(Z> ___) then you should subtract the 0.5 to extend the interval and if P(Z< _____) then you should add the 0.5 to extend the interval. so, what's up with the screen shot I've attached?

What am I missing?
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Old 02-13-2019, 02:14 PM
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When you approximate with a normal using continuity correction, you approximate the CDF by adding 0.5 (minus the mean all over the standard deviation). A “strictly greater than” probability is the complement of this.
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Old 02-13-2019, 02:57 PM
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Quote:
Originally Posted by Colymbosathon ecplecticos View Post
Remember from calculus that definite integrals are limits of Riemann sums?

A continuous distribution, such as the normal, is really a limit of Riemann sums.

We want to approximate a discrete distribution by a continuous one. The idea is that we will represent our discrete distribution as a histogram (an ogive, technically). We need to know where to center those rectangles. The best place to put them (in some sense) is to center them on the integers. That in turn implies that we break the real numbers up into unit intervals centered at the integers.

Upshot: You want all Poisson random variables greater than 10? Approximate by a normal greater than 10.5. Why? Because you don't want 10 included.

Want all of them less than or equal to 10? Approximate by a normal less than 10.5. Why? Because you do want 10 included.


Want 10 itself? Approximate by 9.5 to 10.5. Why? Because this is the interval that represents 10.
Sorry to quote myself Ö.
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Old 02-13-2019, 05:34 PM
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Quote:
Originally Posted by masweeney718 View Post
I'm using Actex to study for P. Taking the test next month.

Please give me a hand here. Continuity correction.....
so this is from the 3rd free exam on TIA. Why do we want P(Z>55.5) rather than P(Z>54.5)? I feel like I've gone through the book every time I do a continuity correction problems. I thought I'd finally understood it and now this comes up...

Based on Actex, I feel like if you are doing P(Z> ___) then you should subtract the 0.5 to extend the interval and if P(Z< _____) then you should add the 0.5 to extend the interval. so, what's up with the screen shot I've attached?

What am I missing?
"More than 55" --> Z > 55. Z > 54.5 adds more than what you're looking for.
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Old 02-14-2019, 11:08 AM
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Itís worth pointing out that this method requires the random variable youíre approximating a probability for to be consecutive integer-valued. I donít think exam P generally has problems where the random variable isnít, but I think Iíve seen it on other exams (maybe STAM?).
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Old 02-25-2019, 01:32 PM
masweeney718 masweeney718 is offline
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AH HA! Thank you!!! its because it says "more than" as opposed to something like "at least" so I don't want it to be equal to 55! THANK YOU THANK YOU THANK YOU! I"ve been staring at the study guide etc and keep seeing the damn +1/2 and -1/2 and just couldn't see it!
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