Question 1171969
<i>a) above 114</i>
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z-score = {{{(114-102)/16}}} = {{{12/16}}} = 0.75
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A z-score of 0.75 is 0.7734.  This means 77.34% of patients have an IQ below 114.  To find the percentage of people with IQs above 114, subtract this from 1. This result is 22.66%. <b>Therefore, 22.66% of patients have an IQ above 114.</b>
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<i>b) between 90 and 118</i>
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z-score1 = {{{(118-102)/16}}} = {{{16/16}}} = 1.00
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A z-score of 1.00 is 0.8413. This means 84.13% of patients have an IQ below 118.
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z-score2 = {{{(90-102)/16}}} = {{{(-12)/16}}} = -0.75
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A z-score of -0.75 is 0.2266. This means 22.66% of patients have an IQ below 90.
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To find the percentage of patients with IQs between 90 and 118, subtract 22.66% from 84.13%. This result is 61.47%.  <b>Therefore, 61.47% of the patients have an IQ between 90 and 118.</b>