Question

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.)

Answer 1

Answer:

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:

$z=\frac{X-\mu}{\sigma}$

We substitute to get:

$-0.675=\frac{X-98.8}{17.1}$

This implies that:

$17.1*-0.675=X-098.8$

$-11.5425=X-098.8$

Solve for x to get:

$x=98.8-11.5425$

X=87.2575