College

Assume that adults have IQ scores that are normally distributed with a mean of 97.8 and a standard deviation of 15.2. Find the first quartile (Q1), which is the IQ score separating the bottom 25% from the top 75%.

The first quartile is:

Answer :

In this problem, we have a normal distribution with:

• mean μ = 97.8,

,

• standard deviation σ = 15.2

The first quartile Q1 is given by the following formula:

[tex]Q_1=\mu-0.675\cdot\sigma\text{.}[/tex]

Replacing the data of the problem, we get:

[tex]Q_1=97.8-0.675\cdot15.2=87.54._{}[/tex]

Answer

The first quartile is 87.54.

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