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: Calculate the z - score

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x = 105$, $\mu=100$, and $\sigma = 15$. So $z=\frac{105 - 100}{15}=\frac{5}{15}\approx0.33$.

Step2: Find the area from the z - table

We want to find $P(X<105)$. Looking up the z - score of $z = 0.33$ in the standard normal distribution table, the area corresponding to $z=0.33$ is $0.6293$.

Answer:

$0.6293$