find the indicated iq score. the graph to the right depicts iq scores of adults, and those scores are…

find the indicated iq score. 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 indicated iq score is . (round to the nearest whole number as needed.)

find the indicated iq score. 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 indicated iq score is . (round to the nearest whole number as needed.)

Answer

Explanation:

Step1: Find the area to the left of x

The area to the right of x is 0.3204. So the area to the left of x, denoted as $A$, is $A = 1 - 0.3204=0.6796$.

Step2: Use the z - score formula

We use the standard normal distribution table (z - table) to find the z - score corresponding to the area 0.6796. Looking up in the z - table, the z - score $z$ corresponding to an area of 0.6796 is approximately $z = 0.47$. The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $\mu = 100$ (mean), $\sigma = 15$ (standard deviation), and we want to find $x$.

Step3: Solve for x

Rearranging the z - score formula $z=\frac{x - \mu}{\sigma}$ gives $x=\mu+z\sigma$. Substitute $\mu = 100$, $z = 0.47$, and $\sigma = 15$ into the formula: $x=100 + 0.47\times15$. $x=100+7.05$. $x = 107.05$.

Answer:

107