<h3>Answer: 49.85% (second answer choice)</h3>
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Explanation:
mu = 214300 = population mean of home values
sigma = 41000 = population standard deviation of home values
Compute the z score for the raw score x = 91300
z = (x-mu)/sigma
z = (91300-214300)/41000
z = -123000/41000
z = -3
This tells us the raw score x = 91300 is exactly 3 standard deviations below the mean.
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Compute the z score for the raw score x = 214300
z = (x-mu)/sigma
z = (214300-214300)/41000
z = 0/41000
z = 0
This is expected as the raw score x = 214300 is exactly at the mean
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Finding P(91300 < x < 214300) is equivalent to computing P(-3 < z < 0)
Recall that the empirical rule states roughly 99.7% of the distribution is within 3 standard deviations of the mean.
In terms of an equation, this means P(-3 < Z < 3) = 0.997 approximately.
Cut 99.7% in half to get (99.7%)/2 = 49.85%
So, P(-3 < Z < 0) = 0.4985 approximately.
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