Assume that adults have IQ scores that are normally distributed with a mean of 98.8 and a standard deviation 17.1. Find the first quartile Q1, which is the IQ score separating the bottom 25% from the top 75%. (Hint: Draw a graph.)

Using the normal distribution, it is found that the IQ score separating the bottom 25% from the top 75% is of 87.

------------------------

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula, which  in a set with mean and standard deviation , is given by:

------------------------

The IQ score is 87.

A similar problem is given at link

The  IQ score separating the bottom 25% from the top 75%. is 87.3

Step-by-step explanation:

Given that adults have IQ scores that are normally distributed with a mean of 98.8 and a standard deviation 17.1.

To find the first quartile, we calculate X such that P(X<z)=0.25.

From the normal distribution table the The z-value that corresponds to an area of 0.25 is z=-0.675

We  use the formula:

We substitute to get:

This implies that:

Solve for x to get:

X=87.2575