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confused about normal approximation

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  • confused about normal approximation

    Hi

    this is my first time in this web site, and it'd be really great if I could get some help from some nice ppl in here!
    So I was doing this problem in the text book,
    and I got confused about the normal approximation. (I think it should be pretty basic, but it's something I just don't get)


    Problem1:
    p1.jpg

    Soln1:
    s1.jpg

    This is pretty straight forward, and I do understand the whole process
    But then,

    Problem2:
    p2.jpg

    Soln2:
    s2.jpg

    You can notice that, for the Problem2, 0.5 was substracted from 15,
    in order to minimize the error occurring when measuring binomial distribution with normal distribution (or whatever else for the reason)

    However, that does not applied to Problem1, 55 stays 55!
    If we substract .5, we'll get an answer of .24 which is not the right answer.
    But then, if we don't substract .5 from Problem2, we get the answer of 0.06, which is not an option.
    But I just want to know when we take the 0.5 off.
    I remember some info from internet that, as long as n is quite large and p is close to 0.5, we use the normal approximation for the binomial.
    But how close is close enough, and how large is large enough?
    It said as long as np>5, it is considered as enough large and close
    But for the Problem1, np is 60, which is quite larger than 5 :skeptical:

    Can anybody give me some insight?
    I'd greatly appreciate that.

  • #2
    it says P[N>=15] = P[N>=14.5] "OH RLY!", luckily I rounded to A and got it right anyway.

    P[N>=15] = 0.0559
    P[N>=14.5] = 0.0764

    The answer = 0.0800

    =======================

    oh, i found this in my notes: good if n> 20 and p<.05 -OR- very good if n>100 and np<10

    1st problem: n=2160, p=0.0278 and np=60
    2nd problem: n=1000, p=0.01 and np=10
    so according to my notes, the second problem borders very good...
    fuzbyone
    Actuary.com - Level I Poster
    Last edited by fuzbyone; July 6 2009, 02:12 AM.
    P FM MFE C

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    • #3
      One thing that confuses me is that the second solution says that the normal tables provided with the exam only go to 1 decimal place and you have to interpolate, but the tables in the demo at http://www.beanactuary.com/exams/practice.cfm have 2 decimal places. Are these solutions really from a book for 1/P?

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      • #4
        Huh? I still dont get it,
        so since np is extremely large (60), we dont round off?
        When do we exactly take off 0.5?

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        • #5
          it says ADDboy has allready passed exam P/1 and several others.

          I'm going to believe ADDboy is correct, and that is not a typical exam P/1 problem to worry about.
          P FM MFE C

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          • #6
            but the error in the table doesn't really explain when we should substract 0.5..
            can u just tell me when we do that? just in general? I'll really appreciate that(_ _)

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            • #7
              Originally posted by fuzbyone View Post
              it says ADDboy has allready passed exam P/1 and several others.

              I'm going to believe ADDboy is correct, and that is not a typical exam P/1 problem to worry about.
              I think it's a perfectly reasonable 1/P problem; I just didn't understand why the book was doing linear interpolation based on 1 decimal place table lookups. I avoided the question in the OP about when to use the continuity correction because I have never seen a clear answer about that on 1/P. On some of the other prelim exams they specifically say to always use it when you have a discrete distribution, but I don't recall seeing that instruction when I took 1/P but that was a while ago.

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