Question 195265: If the average price of a new home is $145,500, find the maximum and minimum prices of the houses that a contractor will build to include the middle 80% of the market. Assume that the standard deviation of prices $1500 and the variable is normally distributed.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! If the average price of a new home is $145,500, find the maximum and minimum prices of the houses that a contractor will build to include the middle 80% of the market. Assume that the standard deviation of prices $1500 and the variable is normally distributed.
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Determine the z-values associated with the middle 80% of a normally-
distributed population.
Draw the picture of a normal curve.
Sketch what appears to be the middle 80% portion.
The top limit has 40% to the right of the mean.
The bottom limit has 40% to the left of the mean
The upper z limit is InverseNorm(0.90) = 1.2816
The lower z limit is InverseNOrm(0.10) = -1.2816
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Now convert these z-scores to raw scores using x = z*sigma + mean
x = 1.2816*1500 + 145,500 = $147,422.33 ( max price )
x = -1.2816*1500 + 145,500 = $143,577.67 (min price )
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Cheers,
Stan H.
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