Question 1152775
z1 = {{{(575 - 550)/(100/sqrt(30))}}} = 1.37
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z2 = {{{(500 - 550)/(100/sqrt(30))}}} = -2.74
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Look up 1.37 on a z-table.  You get 0.9137.  This is the probability the mean score is less than 575.
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Look up -2.74 on a z-table.  You get 0.0031.  This is the probability the mean score is less than 500.
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To find the probability that the mean score is between 500 and 575, simply subtract 0.0031 from 0.9137.  You get an answer of 0.9106.  
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<b>This means there is a 0.9106 probability that the mean score is between 500 and 575.</b>