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Percentile Question

  1. Aug 29, 2009 #1
    I am not exactly sure what I am supposed to do to solve this problem:

    The weight of people in a certain pacific island is normally distributed with a mean of 175 lb and a standard deviation of 33 lb. They want to design a one person canoe that will be able to serve 85% of the island's people. What should be the carrying capacity of the canoe?

    Ok I know I wouldn't use a CI to solve this problem, but I am not sure what the exact setup would be. I have a hunch that I would use the percentiles where the Z critical value would be 1.04 using Z 15.

    Where do I go from there?
     
  2. jcsd
  3. Aug 29, 2009 #2
    Use the percent given to find the corresponding z score. You have population mean & standard deviation, as well as the z score, so you can solve for the unknown
     
  4. Aug 29, 2009 #3
    Ok...

    [tex]z= \frac{(x-\mu)}{\sigma}[/tex]

    [tex]1.04= \frac{(x- 175)}{33}[/tex]

    x = 209.32

    This doesn't sound right to me at all with the s.d. and mean?
     
  5. Aug 29, 2009 #4

    Math Is Hard

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    It looks right to me because if you were to go only one standard deviation up (z = 1), the x score would be 175 (M) + 33 (1 standard dev) = 208. At the 85th percentile, your z score (1.04) is just a little bit higher than that.
     
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