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I am trying to see if it possible to derive a bell curve for a profession's annual salary. If I know how many people are part of the profession (such as 30,000 persons) and I know the mean annual salary (such as \$234,000) and that I know that the lowest 10% earn \$143,000, how can I derive a bell curve to find out what the highest 10% earn?

José Carlos Santos
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Tienth
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    Welcome to MSE. Please read this text about how to ask a good question. – José Carlos Santos Apr 13 '21 at 02:05
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    Assuming such a distribution is normal... yeah. Just need to do some z-score manipulations. The z-score you seek is $-1.28.$ Now use the usual transformation $x = \mu + z \sigma$ and solve for the standard deviation. – Sean Roberson Apr 13 '21 at 02:12
  • I wouldn't assume the distribution of salary is normal. If you have access to all the data I suggest developing a relative frequency histogram or a relative frequency polygon to see if its even appropiate to fit your data with a normal curve. Quantitative variables like "salary" often generate datasets that are skewed right. – Matthew H. Apr 13 '21 at 03:37

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HINTS

  • How many parameters do you need to specify the actual Gaussian curve you will be working with (see Normal distribution on Wikipedia)?
  • Can you find one of them directly from the data you cited? (Think of mean annual salary)?
  • Can you approximate the other one using the $10\%$ bound you cite?

Now that you know both parameters, specifying the distribution is straight-forward.

gt6989b
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