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Basic Statistics Homework Question

  1. Oct 19, 2014 #1
    Mod note: This post was moved from another forum section, so doesn't use the homework template.
    A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 8.7 hours.

    Is this the same as P(X-bar > 8.7) and P(Z > .16666666666..) because then the answer would be about 43% and the answers given are:

    0.1469
    0.1346
    0.1946
    0.1285


    Can someone explain what I am doing wrong? Thanks in advance for your replies.
     
    Last edited by a moderator: Oct 19, 2014
  2. jcsd
  3. Oct 19, 2014 #2

    Mark44

    Staff: Mentor

    Please show your calculation for z. I'm pretty sure that's where the problem lies.
     
  4. Oct 19, 2014 #3
    Mean= 8.4
    x=8.7
    SD=1.8

    1.8%3D%200.16666666666666666666666666666667.gif
     
    Last edited by a moderator: Apr 19, 2017
  5. Oct 19, 2014 #4

    Mark44

    Staff: Mentor

    You have a sample of 40 mechanics. How does that need to fit into your calculations?
     
  6. Oct 19, 2014 #5
    That is where I am stuck and unsure of what to do. Do I raise the probability of getting one mechanic whose time exceeds 8.7 to the power of 40?

    So that would be gif.latex?.433816%5E4%5E0.gif ?
     
  7. Oct 19, 2014 #6

    Mark44

    Staff: Mentor

    No, that's not it. Your sample size (40) affects the standard deviation you use to calculate z. Your book should have this formula. As I recall, it's called the standard error of the mean, and represents the s.d. of all samples of size n.

    BTW, I noticed that you also posted this question in the Precalc section. That's a no-no to post the same question in two or more forum sections.
     
  8. Oct 19, 2014 #7
    I just found the equation in my book they dedicated such a little piece of text to it that I missed it when reading the first time. I calculated the standard error to of the mean to be 40%3D%200.28460498941515413987990041899894.gif Where do I go from this step?
     
  9. Oct 19, 2014 #8

    Mark44

    Staff: Mentor

  10. Oct 20, 2014 #9
    Both my book and the Wikipedia link gives the same formula for calculating the error of the mean: Error of the mean= variance/sample size. When I do the calculations I get ex%3F3.24%2F40%253D%25200.28460498941515413987990041899894&hash=b7bb1ba2c30b7b6dfd3eb8b7ebaa6ef7.png . I don't see how I can apply that number to solving this problem. Is this the new standard deviation that I use to calculate the z-score?
     
  11. Oct 20, 2014 #10
    ^ Actually that's exactly what I needed to do haha. I don't quite understand why it works that way though. Can anyone explain it?
     
  12. Oct 20, 2014 #11

    Mark44

    Staff: Mentor

    In the Wiki link, it gives this: ##S.E. = \frac{s}{\sqrt{n}}##
    Your calculation apparently doesn't include the square root.
    You use it when you're looking at how samples of a given size are distributed.
    From the Wiki page (emphasis added):
     
  13. Oct 20, 2014 #12

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Your elementary arithmetic is wrong: 3.24/40 = 0.081 exactly, nowhere near 0.28460...... . Anyway, it is unscientific nonsense to keep 20-30 decimal digits of accuracy in such problems, especially as the 3.24 might not have even full two-decimal accuracy (being based on limited observations). Sometimes you should keep several additional decimals of accuracy during a calculation, to guard against roundoff errors, but keeping the kind of (20+ digits) accuracy you done---especially in a number that is so wrong---is something you should avoid.
     
  14. Oct 20, 2014 #13
    Sorry I forgot to say that I took the square root of the answer 0.081. Anyways I have solved this problem. This thread can be closed.
     
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