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Question 494:



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The middle 80% would mean that 10% of the house sell for greater than some amount and 10% sell for less than some amount. So we want to find the z-score associated with a 2-sided area of 20%. We can use the percentile to z-score calculator and enter .80 and select 2-sided. This gets us a z-score of 1.28. If we enter .20, we get -1.28.

Now we just need to find the  prices for z-score of 1.28 and -1.28. We can do this by setting up an equation and solving for the unknown using the z-score formula (datapoint - mean)/standard deviation.

  1. (x-145,000)/1500 = 1.28
  2. (x-145,000) = 1920
  3. x = 146920

Then for the negative:

  1. (x-145,000)/1500 = -1.28
  2. (x-145,000) = -1920
  3. x = 143080

So prices the minimum price of 143,080 and the maximum price of 146,920 will represent the middle 80% of that market.

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