document.write( "Question 1143990: the average price of new story townhouse is 1,600,000, find the maximum and minimum prices of the townhouse that a contractor will build to include the middle 70% of the market. Assume that the standard deviation of prices is 300,000 and the variable is normally distributed. \n" ); document.write( "
Algebra.Com's Answer #764966 by Theo(13342)\"\" \"About 
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the mean is 700,000
\n" ); document.write( "the standard deviation is 300,000
\n" ); document.write( "use the z-score formula to find the low and high z-score where 70% of the prices are in the middle of the normal distribution curve.
\n" ); document.write( "in the normal distribution curve, 70% in the middle means that 30% are outside the limits which means that 15% are to the left of the middle and 15% are to the right of the middle.
\n" ); document.write( "since the z-score tables give you the are to the left, you would look for a z-scored that has 15% of the area to the left of it and you would look for a z-score that have 85% of the area to the left of it.
\n" ); document.write( "alternatively, you can use a z-score calculator to find the same, since it is much more accurate when the areas in the table are not right on.
\n" ); document.write( "one such calculator can be found at https://stattrek.com/online-calculator/normal.aspx
\n" ); document.write( "using this calculator, i get the following z-scores for the 15% to the left and the 85% to the left of the z-score.
\n" ); document.write( "the low z-scorei is -1.036.
\n" ); document.write( "the high z-score is 1.036.
\n" ); document.write( "the z-scores are the same except for the sign because the normal distribution curve is symmetric about the mean.
\n" ); document.write( "now that you have the z-scores, you find the raw scores by using the z-score formula of z = (x-m)/s
\n" ); document.write( "z is the z-score.
\n" ); document.write( "x is the raw score.
\n" ); document.write( "m is the raw mean.
\n" ); document.write( "s is the standard deviation.
\n" ); document.write( "for the low z-score, the formula becomes -1.306 = (x-1,600,000)/300,000.
\n" ); document.write( "solve for x to get x = -1.036 * 300,000 + 1,600,000 = 1,289,200.
\n" ); document.write( "for the high z-score, the formula becomes 1.036 * 300,000 +1,600,000 = 1,910,800.
\n" ); document.write( "that's those are your solutions.
\n" ); document.write( "this can be seen visually in the following display.
\n" ); document.write( "any differences in the numbers is due to differences in rounding between the two calculators used.
\n" ); document.write( "the calculator used in the display can be found at http://davidmlane.com/hyperstat/z_table.html
\n" ); document.write( "the first pictures below are finding the z-score and the third picture below is the visual display of the results.\r
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