Question

find the area of the shaded region. the graph to the right depicts iq scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. click to view page 1 of the table. click to view page 2 of the table. the area of the shaded region is
(round to four decimal places as needed.)

Explanation:

Step1: Identify the distribution and parameters

We have a normal distribution with mean $\mu = 100$ and standard deviation $\sigma = 15$. We need to find the area to the right of $x = 110$ (assuming the shaded region is to the right of 110, as per the graph with 110 marked). First, calculate the z - score. The formula for the z - score is $z=\frac{x-\mu}{\sigma}$.
Substitute $x = 110$, $\mu = 100$, and $\sigma = 15$ into the formula: $z=\frac{110 - 100}{15}=\frac{10}{15}=\frac{2}{3}\approx0.67$ (rounded to two decimal places).

Step2: Find the area using the standard normal table

The standard normal table gives the area to the left of a z - score. We want the area to the right of $z = 0.67$. The area to the left of $z = 0.67$ can be found from the standard normal table. Looking up $z = 0.67$ in the standard normal table, the area to the left is approximately 0.7486.
The area to the right of $z$ is $1 -$ (area to the left of $z$). So, the area to the right of $z = 0.67$ is $1 - 0.7486=0.2514$.

Answer:

0.2514