Question 1150804
Z-score = {{{(7.5 - 6)/3}}} = {{{1.5/3}}} = 0.5
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Look up 0.5 on a z-table.  The result is 0.6915.  This means there is a 0.6915 probability the random variable will be below 7.5.
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Z-score = {{{(5.7 - 6)/3}}} = {{{(-0.3)/3}}} = -0.1
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Look up -0.1 on a z-table.  The result is 0.4602.  The means there is a 0.4602 probability the random variable will be below 5.7.
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The find the probability the random variable will be between 7.5 and 5.7, simply subtract the two probabilities we found (above) from one another:
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{{{0.6915 - 0.4602}}} = 0.2313
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So, there is a 0.2313 probability the random variable will fall between 7.5 and 5.7.