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Normal distribution percentage problem.

  1. Apr 11, 2012 #1
    1. The problem statement, all variables and given/known data
    A company pays its employees an average wage of $3.25 an hour with a standard deviation of sixty cents. If the wages are approximately normally distributed, determine
    the minimum wage of the employees who are paid the highest 5%.

    2. Relevant equations
    z=(x-μ)/σ

    3. The attempt at a solution
    I did:
    .95=((x-3.25)/.6) which equals .57=x-3.25
    therefore x=3.82. I feel like I didn't do this correctly and I can't finish the rest of my homework if I don't know what I'm doing. Thanks.
     
    Last edited: Apr 11, 2012
  2. jcsd
  3. Apr 11, 2012 #2
    Isn't that equation for standardizing your values? 95% has nothing to do with z-scores.
     
    Last edited: Apr 11, 2012
  4. Apr 11, 2012 #3
    Oh, shoot, you're right. Well how would I find out what 95% of the wages cause I don't have the slightest clue.
     
  5. Apr 11, 2012 #4
    Your z-value is +-σ from the mean. What is 95% in terms of σ on a normal distribution? Also, do you use calculators to help you in your class? If you do, this question should be quite straightforward.
     
  6. Apr 11, 2012 #5

    Ray Vickson

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    Homework Helper

    If z_95 is the 95th percentile of the standard normal (which is available in tables or on some calculators) you need [tex] z_{95} = \frac{x-3.25}{0.6}.[/tex] Note: you should divide by 0.6 not 6, since 0.6 is the standard deviation in dollars.

    RGV
     
  7. Apr 11, 2012 #6
    No, my teacher wants us only using this table she gave us.
     
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