Expert: Sherry Wallin - 2/3/2011

Question
The monthly incomes of a group of 10,000 persons were found to be normally distributed with mean equal to  15,000 and standard deviation equal to  1000. What is the lowest income among the richest 250 persons?

Answer
Sayali~
Of the 10,000 persons the richest are the persons numbered
9751 - 10,000, so person 9751 has the lowest income of the richest 250 persons. If you look at the ratio of 9750 to 10,000 you find it is .975 is where the 9750th persons income is. By the Empirical Rule 99.7% of all the data falls within 3 standard deviations of the mean, and that means that 3*1000 added to the mean of 15000 and 3*1000 subtracted from the mean gives us the interval for which 99.7% of the data falls into or the interval (12000, 18000) that 99.7% of the incomes are in. So it stands to reason that .975 of 18000 is the lowest income of the top 250 richest, which by simple math is $17,550. This is only indirectly using statistics to answer the question but the math is solid behind the statistical concepts being used.

Math Prof

PS I am sure there are methods that are simpler that require less of an understanding of what is happening mathematically but I choose to use mathematics to determine this answer coupled with a few well known statistical concepts.