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Assume that adults have IQ scores that are normally distributed with a mean of 96.296.2 and a standard deviation 20.520.5. Find the first quartile Upper Q 1Q1​, which is the IQ score separating the bottom​ 25% from the top​ 75%.

User Cbarrick
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1 Answer

5 votes

Answer:

The first quartile of the IQ scores of adults is 82.26.

Explanation:

The first quartile is the value that is greater than 25% of the observations and less than 75% of the observation.

The formula to compute the first quartile (Q₁) of a Normal distribution is:


Q_(1)=\mu-0.68\sigma

The mean and standard deviation of the IQ scores of adults are:


\mu=96.2\\\sigma=20.5

Compute the first quartile value as follows:


Q_(1)=\mu-0.68\sigma=96.2-(0.68*20.5)=82.26

Thus, the first quartile of the IQ scores of adults is 82.26.

User Mikael Lirbank
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