Question

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%.

Answer 1

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.