SOLUTION: A psychologist finds that the intelligence quotients of a group of patients are normally distributed, with a mean of 102 and a standard deviation of 16. Find the percent of the p

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Question 1171969: A psychologist finds that the intelligence quotients of a group of patients are
normally distributed, with a mean of 102 and a standard deviation of 16. Find
the percent of the patients with IQs
a) above 114.
b) between 90 and 118.
Answer by VFBundy(438) About Me  (Show Source):
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a) above 114

z-score = %28114-102%29%2F16 = 12%2F16 = 0.75

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%. Therefore, 22.66% of patients have an IQ above 114.

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b) between 90 and 118

z-score1 = %28118-102%29%2F16 = 16%2F16 = 1.00

A z-score of 1.00 is 0.8413. This means 84.13% of patients have an IQ below 118.

z-score2 = %2890-102%29%2F16 = %28-12%29%2F16 = -0.75

A z-score of -0.75 is 0.2266. This means 22.66% of patients have an IQ below 90.

To find the percentage of patients with IQs between 90 and 118, subtract 22.66% from 84.13%. This result is 61.47%. Therefore, 61.47% of the patients have an IQ between 90 and 118.