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Math Help - Normal Distribution Question.

  1. #1
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    Normal Distribution Question.

    Hello everyone! Thanks in advance for any help you can give me. I am in my first year of college, currently taking a MAT 103 class (Quantitative Reasoning). We are starting to get into sections that introduce the basics of prob and stats. Very basic stuff in the scheme of things and no where near the level most people here are getting help with (hopefully I will be there one day). I have a test tomorrow and despite understanding the vast majority of this section, one area in particular is giving me massive amounts of grief.


    The problem is relating to Normal Distribution. For what ever reason, this section completely lost me. Things involving the 68-95-99.7 (empirical? rule), bell curves, z-scores, etc etc etc. I am going to post two questions from the study guide that I am struggling with the most. My professor is pretty awesome and gives us pretty much exactly what will be on the test, just with different numbers swapped out to see if we know the process.


    1. The time it takes Claudia to drive to work is normally distributed with a mean of 46 minutes and a standard deviation of 7 minutes. What percentage of time will she be able to drive to work in less than 60 minutes?

    2. Weights of adult females are normally distributed with a mean of 138 lb and a standard deviation of 15 lb. A weight of 150 lb represents what percentile? Round the percentile to the nearest tenth.


    Normally I would shoot my professor an email or try to get help in class, test is the first day back from spring break though and I did not manage time wisely before class ended (shame on me I know). Anyways, here are my issues with each of those problems.


    The first I just completely do not understand the process at all. The drawing of the bell curve and what it symbolizes, the 68-95-99.7 rule, etc etc etc. I understand the standard deviation bit where "7 minutes" goes before and after the time or something to that degree. I do not understand much past that as to why you draw the curve or how you know which rule it falls into, my notes just confuse the heck out of me!


    The second problem I understand how to solve using the z-score. That part of looking up the percentile and what not is easy to me. My question is how do I know that I need to use the Z-Score? For that one I just knew it because I have it memorized on the study guide, with a random problem on the test what are the clues to make it click? I recall from a problem in class we were working through doing the bell curve, the professor said the 68-95-99.7 rule would not apply and we would have to use the z-score. What about a problem would make it not apply and cause you to be aware you have to solve it using the z-score?




    I explained it as best as I could, I am a pretty big newbie when it comes to this type of math, so forgive the ignorance haha. Any help at all would be greatly appreciated and I thank you for your time. If what I am saying still does not make sense I can scan the notes and examples the professor gave that might show it a bit more in-depth. Thanks!
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  2. #2
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    Re: Normal Distribution Question.

    Both of your problems should be solved with a Q function table (both of them basically ask the same thing but with different values).

    P(X \leq x) = Q\left (\frac{x-\mu}{\sigma} \right)
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  3. #3
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    Re: Normal Distribution Question.

    1. The time it takes Claudia to drive to work is normally distributed with a mean of 46 minutes and a standard deviation of 7 minutes. What percentage of time will she be able to drive to work in less than 60 minutes?
    Lewisite:
    The mean, of course, is an average. So if you sum all the numbers (all the times Claudia drives to work) and divide by the amount of times you get 46 minutes. But that does not mean that it took 46 minutes each time. Some times it took less time and other times longer. That's where the standard deviation kicks in. It explains the variability or variation of all the times that she kept tabs.
    The empirical rule 68/95/99.7 tells us that for example 68 % of the time it will take her within one std dev of the mean. Since the mean is 46 and the sd=7 if we subtract 7 from the mean we get 48-7=41 if we add 7 to the mean we get 48+7=55. So 68% of the time she will need between 41 and 55 minutes.
    Similarly using 2 std devs. 48-2(7)=48-14=34 and 48+2(7)=48+2(7)=62 So 95% of the time she will need between 34 and 62 minutes.

    By changing 60 minutes in the question to standard deviation units (that's the z-score) and using an appropriate table, you can get the percentage for less than 60 minutes.
    z=(x-mean)/std dev z=(60-48)/7 z=12/7 z=1.71 Using a table of areas (percentages) under the normal curve (probably on the inside cover of your text but definitely in your text) you'll see
    .9564 or 95.64%
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