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According to the National Association of Realtors, the mean sale price for existing homes in the United States in 2011 was $214,300. Assume that sale prices are normally distributed with a standard deviation of $41,000. Find the percentage of existing homes in 2011 that sold for between $173,300 and $296,300?

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82% of the existing homes in 2011 are sold between $173,300 and $296,300.

Step-by-step explanation:

  • mean sale price, M = $214,300
  • standard deviation, SD = $41,000
  • The sale prices are normally distributed.

The left side of the mean ⇒ 34% = M-SD, 14% = M-2SD, 2% = M-3SD

  • 34% ⇒ M-SD = 214,300-41,000 = 173,300

The right side of the mean ⇒ 34% = M+SD, 14% = M+2SD, 2% = M+3SD

  • 34%⇒ M+SD = 214,300+41,000 = 255,300
  • 14%⇒ M+2SD = 214300+2(41,000) = 296,300

The percentage of existing homes in 2011 that sold for between $173,300 and $296,300 is 34%+34%+14% = 82%

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