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Frustrations in Statistics
Mon Mar 06 2006

I have one example problem in my Statistics homework that is driving me nuts. It goes something like this:

The lengths of the lake trout in a lake are believed to have a normal distribution with a mean of 15.6 inches and a standard deviation of 3.8 inches. What is the probability of you catching a fish less than 15 inches long?

Now, if I understand the chapter correctly, I should be able to find this with the following formula:

[x(bar) - mu]/sigma which translates to (15 - 15.6)/3.8 giving me an answer of -0.158

That is all fine and dandy except the fact that the answer is supposed to be 0.4364 (a.k.a. a probability of about 44%)

We were told to use a handy table that gives The Area Of Normal Distribution (which can be found here under the Standard Normal (Z) Table)tells me that the area for this should be .0596, but does not tell how it is to be used with this problem. Do I add this value to my answer? Subtract it to something? divide it by everything? Who knows? Every combination I could think of and try with the answer I got still results in less than correct answers. It doesn't help that there is barely a reference to this table in the chapter, and what reference there is does not explain or demonstrate how this table comes into use.

I'm WAAAAAAAAAAAAAY beyond realizing that I will never be a Statistician.


Progress


Well, I got my homework for my Stat class finished and sent off to the instructor, now I just need to wait for him to e-mail out the final so I can take care of that.
As far as my final for my Discrete Math class, it is a take home test, and I think I am done with it. I just need to find a way to verify my answers before I take it in to my instructor. Once again I’m worried about this test. It seemed easy to me, and that makes me concerned that I completely botched it. Once I have my books handy at the same time as I’m on my computer, I’ll try to remember to post some of the problems so you can all see what I’m dealing with, or for those of you who need to take this class and haven’t yet, you can see what you’re in for!

Doesn’t that sound fun?


8 Comments
  • From:
    FutureCat (Legacy)
    On:
    Mon Mar 06 2006
    Ah, ok, now I can see where you're getting confused.

    First thing, you're using your table wrong. To look up 0.16 (which is 0.158 rounded), you go down the side (which gives you your first digit) to 0.1 (not 1.6 as you did), then you go along that row to the column with 0.06 at the top (which is your second digit). That gives you 0.0636. You've now converted your z-score to a probability, so you can forget about the 0.158 now, you don't need it any more.

    Now look at the little diagram at the top of the table. That shows you which probability you've just found. 0 is the mean, and a is the z-score you calculated (x-mu/sigma). Remember that the z-score is just a way of shifting your data so that your mean (which was 15.6) is now 0 and your standard deviation (which was 3.8) is now 1. The part that's coloured in is between the 0 and the a, so that diagram tells you that you've now got the probability of a fish being between the mean and your z score, ie. being between 15.6 and 15 inches. But you want to know the probability of it being less than 15 inches. So the part of the curve you want to be coloured in is the other side of the line marked a.

    The part that is coloured in plus the part you want coloured in add up to half the curve, i.e. a probability of 0.5. The part that's coloured in has a probability of 0.0636 (from the table), so we know that the part you want coloured in must be the rest of that 0.5. So all you need to do is subtract 0.036 from 0.5 to give you the remaining probability, which is 0.4364.

    Clear as mud?

    ^ ^
    00
    =+=
    v
  • From:
    FutureCat (Legacy)
    On:
    Mon Mar 06 2006
    Oops, I've just realised I was looking at a different normal distribution table to you (the numbers are the same, but the labeling on the diagram is different), so I've probably completely confused you! Everywhere I said "a" up above, change it to "z".

    ^ ^
    00
    =+=
    v
  • From:
    Pragmatist (Legacy)
    On:
    Mon Mar 06 2006
    But you need statistics to complete your degree. Were I the one taking the course, I'd find a different course of study. Actually, I wouldn't be in a course like this in the first place.

    People who "do" math are awesome!

    Shalom
  • From:
    Welshamethyst (Legacy)
    On:
    Mon Mar 06 2006
    ewwwwwww. I'd surely fail. What was 2+2 again?
  • From:
    Yetzirah (Legacy)
    On:
    Tue Mar 07 2006
    Statistically speaking, I am in the 67th percentile when it comes to math.

    My sympathies.
  • From:
    Sezrah (Legacy)
    On:
    Tue Mar 07 2006
    i still have the odd dream about doing maths problems back in school. i used to adore maths and was in the top class at high school, unfortunately thats many many years ago now and thus the time has rendered my maths passion impotent as i can't remember anything from back then and would have to start all over again from scratch

    sez
  • From:
    Kittydragon105 (Legacy)
    On:
    Tue Mar 07 2006
    1.5 seconds after trying to figure out how to solve the problem you mentioned, my brain exploded.

    Neeless to say, I probably won't be a statistician, either.

    Advanced math is way beyond my capabilities. I admire you for going into that kind of field, I definitely couldn't do it!
  • From:
    DancingButterfly (Legacy)
    On:
    Tue Mar 07 2006
    *Shudders* I can't help you with stats!!!!
    *Runs and hides behind a bush* :)
    I do hope that you post the answer to that problem :)