SOLUTION: IQs are normally distributed with a mean of 100 and a standard deviation of 15. If an individual is randomly selected, find the probability that his or her IQ is greater than 12

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Question 251830: IQs are normally distributed with a mean of 100 and a standard deviation of 15.
If an individual is randomly selected, find the probability that his or her IQ is greater than 120.
Find the IQ that separates the lower 70% of the scores from the upper 30%.
Find the probability that 64 randomly selected people who have an average IQ that is greater than 105.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
IQs are normally distributed with a mean of 100 and a standard deviation of 15.
If an individual is randomly selected, find the probability that his or her IQ is greater than 120.
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z(120) = (120-100)/15 = 20/15 = 1.3333
P(x > 120) = P(z > 1.3333) = 0.0912
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Find the IQ that separates the lower 70% of the scores from the upper 30%.
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The z-value that has a left tail of 0.70 is invNorm(0.7) = 0.5244
x = z*sigma + mu
x = 0.5244*15 + 100
x = 107.87
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Find the probability that 64 randomly selected people who have an average IQ that is greater than 105.
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For samples of size 64 the standard deviation is 15/sqrt(64) = 1.8750
z(105) = (105-100)/1.8750 = 2.6667
P(x > 106) = P(z > 2.6667) = 0.0038
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Cheers,
Stan H.