Assume that adults have IQ scores that are normally distributed with a mean of 99.5 and a standard deviation 20.6. Find the first quartile Upper Q 1, which is the IQ score separating the bottom 25% from the top 75%.

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31-05-2018
Mathematics

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Assume that adults have IQ scores that are normally distributed with a mean of 99.5 and a standard deviation 20.6. Find the first quartile Upper Q 1, which is the IQ score separating the bottom 25% from the top 75%.

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11beehshahbaz 11beehshahbaz · Answer 1 · 2018-05-31T23:51:39+02:00

Population Mean = u = 99.5
Population standard Deviation = s = 20.6
We want to find the first Quartile Q1 which is the value with 0.25 percentile score.

First we will find the z value corresponding to 0.25 percentile. From the z table this value comes out to be z = -0.674

The formula to calculate z score is:

[tex]z= \frac{x-u}{s} [/tex]

We want to find the value of x. This is the value of First Quartile Q1. Using the values in the above equation, we get:

[tex]-0.674= \frac{x-99.5}{20.6} \\ \\ x=85.6[/tex]

Rounding to one decimal point, 85.6 is the value of first quartile.

Assume that adults have IQ scores that are normally distributed with a mean of 99.5 and a standard deviation 20.6. Find the first quartile Upper Q 1​, which is the IQ score separating the bottom​ 25% from the top​ 75%.

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Assume that adults have IQ scores that are normally distributed with a mean of 99.5 and a standard deviation 20.6. Find the first quartile Upper Q 1, which is the IQ score separating the bottom 25% from the top 75%.