find the area of the shaded region. the graph to the right depicts iq scores of adults, and those scores are…

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. the area of the shaded region is (round to four decimal places as needed.)

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. the area of the shaded region is (round to four decimal places as needed.)

Answer

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 90$, $\mu=100$, and $\sigma = 15$. So $z=\frac{90 - 100}{15}=\frac{- 10}{15}\approx - 0.67$.

Step2: Find the area to the left of the z - score

We use the standard normal distribution table. The area to the left of $z=-0.67$ is approximately $0.2514$.

Step3: Find the area of the shaded region

The total area under the normal - curve is 1. The area of the shaded region (area to the right of $x = 90$) is $1 - 0.2514=0.7486$.

Answer:

$0.7486$